How to find the volume of a net - ISEE Middle Level Quantitative Reasoning

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Question

Which is the greater quantity?

(a) The sidelength of a cube with surface area $600 \textrm{ cm}^{2}$

(b) The sidelength of a cube with volume $1,000 \textrm{ cm}^{3}$

Answer

(a) A cube has six faces, each a square. Since the surface area of this cube is $600 \textrm{ cm}^{2}$ , each face has one-sixth this area, or $100 \textrm{ cm}^{2}$ ; the sidelength is the square root of this, or $10 \textrm{ cm}$ .

(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:

$\sqrt[3]{1,000} = 10 \textrm{ cm}$

The cubes have the same sidelength.

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Question

Which is the greater quantity?

(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters

(b) The volume of a cube with sidelength 300 millimeters

Answer

(a) The volume of the prism is the product of its length, its width, and its height:

$V = 60 \times 30 \times 15 = 27,000 \textrm{ cm}^{3}$

(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:

$V = 30 ^{3} = 30 \times 30 \times 30 = 27,000 \textrm{ cm}^{3}$

The volumes are equal.

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Question

Give the volume of the box in cubic inches.

Answer

Use the volume formula, substituting :

$V=22 \cdot 12 \cdot 12 = 3168^{3}$

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Question

Give the volume of the above box in cubic centimeters.

Answer

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the volume formula, substituting :

$V = 90 \cdot 60 \cdot 60 = 324,000$ cubic centimeters

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Question

A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?

Answer

The volume of the cube is $20 ^{3} = 20 \times 20 \times 20 = 8,000$ cubic centimeters. Multiply by the number of grams per cubic centimeter to get $8,000 \times 8.9 = 71,200$ grams, or $71,200 \div 1,000 = 71.2$ kilograms.

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Question

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.

Answer

Divide each dimension in inches by 12 to convert from inches to feet:

$L = 24 \div 12 = 2$ feet

$W = 18 \div 12 = 1 \frac{1}{2} = \frac{3}{2}$ feet

$H = 15 \div 12 = 1 \frac{1}{4} = \frac{5}{4}$ feet

Multiply the three to get the volume:

$V = LWH = 2 \cdot \frac{3}{2} \cdot \frac{5}{4} = \frac{15}{4} = 3 \frac{3}{4}$ cubic feet

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Question

The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?

Answer

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is

$50 \times 35 \times 6 = 10,500$ cubic feet.

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Question

One cubic foot is equal to (about) 7.5 gallons.

The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?

Answer

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is

$50 \times 35 \times 7 =12,250$ cubic feet.

One cubic foot is equal to about 7.5 gallons, so multiply:

$12,250 \times 7.5 = 91,875$ gallons.

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Question

Which is the greater quantity?

(a) The sidelength of a cube with surface area $600 \textrm{ cm}^{2}$

(b) The sidelength of a cube with volume $1,000 \textrm{ cm}^{3}$

Answer

(a) A cube has six faces, each a square. Since the surface area of this cube is $600 \textrm{ cm}^{2}$ , each face has one-sixth this area, or $100 \textrm{ cm}^{2}$ ; the sidelength is the square root of this, or $10 \textrm{ cm}$ .

(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:

$\sqrt[3]{1,000} = 10 \textrm{ cm}$

The cubes have the same sidelength.

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Question

Which is the greater quantity?

(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters

(b) The volume of a cube with sidelength 300 millimeters

Answer

(a) The volume of the prism is the product of its length, its width, and its height:

$V = 60 \times 30 \times 15 = 27,000 \textrm{ cm}^{3}$

(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:

$V = 30 ^{3} = 30 \times 30 \times 30 = 27,000 \textrm{ cm}^{3}$

The volumes are equal.

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Question

Give the volume of the box in cubic inches.

Answer

Use the volume formula, substituting :

$V=22 \cdot 12 \cdot 12 = 3168^{3}$

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Question

Give the volume of the above box in cubic centimeters.

Answer

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the volume formula, substituting :

$V = 90 \cdot 60 \cdot 60 = 324,000$ cubic centimeters

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Question

A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?

Answer

The volume of the cube is $20 ^{3} = 20 \times 20 \times 20 = 8,000$ cubic centimeters. Multiply by the number of grams per cubic centimeter to get $8,000 \times 8.9 = 71,200$ grams, or $71,200 \div 1,000 = 71.2$ kilograms.

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Question

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.

Answer

Divide each dimension in inches by 12 to convert from inches to feet:

$L = 24 \div 12 = 2$ feet

$W = 18 \div 12 = 1 \frac{1}{2} = \frac{3}{2}$ feet

$H = 15 \div 12 = 1 \frac{1}{4} = \frac{5}{4}$ feet

Multiply the three to get the volume:

$V = LWH = 2 \cdot \frac{3}{2} \cdot \frac{5}{4} = \frac{15}{4} = 3 \frac{3}{4}$ cubic feet

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Question

The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?

Answer

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is

$50 \times 35 \times 6 = 10,500$ cubic feet.

Compare your answer with the correct one above

Question

One cubic foot is equal to (about) 7.5 gallons.

The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?

Answer

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is

$50 \times 35 \times 7 =12,250$ cubic feet.

One cubic foot is equal to about 7.5 gallons, so multiply:

$12,250 \times 7.5 = 91,875$ gallons.

Compare your answer with the correct one above

Question

Which is the greater quantity?

(a) The sidelength of a cube with surface area $600 \textrm{ cm}^{2}$

(b) The sidelength of a cube with volume $1,000 \textrm{ cm}^{3}$

Answer

(a) A cube has six faces, each a square. Since the surface area of this cube is $600 \textrm{ cm}^{2}$ , each face has one-sixth this area, or $100 \textrm{ cm}^{2}$ ; the sidelength is the square root of this, or $10 \textrm{ cm}$ .

(b) The volume of a cube is the cube of its sidelength, so we take the cube root of the volume of this cube to get the sidelength:

$\sqrt[3]{1,000} = 10 \textrm{ cm}$

The cubes have the same sidelength.

Compare your answer with the correct one above

Question

Which is the greater quantity?

(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters

(b) The volume of a cube with sidelength 300 millimeters

Answer

(a) The volume of the prism is the product of its length, its width, and its height:

$V = 60 \times 30 \times 15 = 27,000 \textrm{ cm}^{3}$

(b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this:

$V = 30 ^{3} = 30 \times 30 \times 30 = 27,000 \textrm{ cm}^{3}$

The volumes are equal.

Compare your answer with the correct one above

Question

Give the volume of the box in cubic inches.

Answer

Use the volume formula, substituting :

$V=22 \cdot 12 \cdot 12 = 3168^{3}$

Compare your answer with the correct one above

Question

Give the volume of the above box in cubic centimeters.

Answer

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the volume formula, substituting :

$V = 90 \cdot 60 \cdot 60 = 324,000$ cubic centimeters

Compare your answer with the correct one above

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How to find the volume of a net - ISEE Middle Level Quantitative Reasoning

Which is the greater quantity? (a) The sidelength of a cube with surface area (b) The sidelength of a cube with volume

Which is the greater quantity? (a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters (b) The volume of a cube with sidelength 300 millimeters

(a) The volume of the prism is the product of its length, its width, and its height: (b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this: The volumes are equal.

Give the volume of the box in cubic inches.

Use the volume formula, substituting :

Give the volume of the above box in cubic centimeters.

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100. centimeters centimeters Use the volume formula, substituting : cubic centimeters

A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?

The volume of the cube is cubic centimeters. Multiply by the number of grams per cubic centimeter to get grams, or kilograms.

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.

Divide each dimension in inches by 12 to convert from inches to feet: feet feet feet Multiply the three to get the volume: cubic feet

The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is cubic feet.

One cubic foot is equal to (about) 7.5 gallons. The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is cubic feet. One cubic foot is equal to about 7.5 gallons, so multiply: gallons.

Which is the greater quantity? (a) The sidelength of a cube with surface area (b) The sidelength of a cube with volume

Which is the greater quantity? (a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters (b) The volume of a cube with sidelength 300 millimeters

(a) The volume of the prism is the product of its length, its width, and its height: (b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this: The volumes are equal.

Give the volume of the box in cubic inches.

Use the volume formula, substituting :

Give the volume of the above box in cubic centimeters.

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100. centimeters centimeters Use the volume formula, substituting : cubic centimeters

A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?

The volume of the cube is cubic centimeters. Multiply by the number of grams per cubic centimeter to get grams, or kilograms.

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.

Divide each dimension in inches by 12 to convert from inches to feet: feet feet feet Multiply the three to get the volume: cubic feet

The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is cubic feet.

One cubic foot is equal to (about) 7.5 gallons. The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is cubic feet. One cubic foot is equal to about 7.5 gallons, so multiply: gallons.

Which is the greater quantity? (a) The sidelength of a cube with surface area (b) The sidelength of a cube with volume

Which is the greater quantity? (a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters (b) The volume of a cube with sidelength 300 millimeters

(a) The volume of the prism is the product of its length, its width, and its height: (b) The volume of the cube is the cube of its sidelength. We restate 300 millimeters as 30 centimeters, and cube this: The volumes are equal.

Give the volume of the box in cubic inches.

Use the volume formula, substituting :

Give the volume of the above box in cubic centimeters.

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100. centimeters centimeters Use the volume formula, substituting : cubic centimeters

Which is the greater quantity?

(a) The sidelength of a cube with surface area $600 \textrm{ cm}^{2}$

(b) The sidelength of a cube with volume $1,000 \textrm{ cm}^{3}$

Which is the greater quantity?

(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters

(b) The volume of a cube with sidelength 300 millimeters

Use the volume formula, substituting :

$V=22 \cdot 12 \cdot 12 = 3168^{3}$

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the volume formula, substituting :

$V = 90 \cdot 60 \cdot 60 = 324,000$ cubic centimeters

The volume of the cube is $20 ^{3} = 20 \times 20 \times 20 = 8,000$ cubic centimeters. Multiply by the number of grams per cubic centimeter to get $8,000 \times 8.9 = 71,200$ grams, or $71,200 \div 1,000 = 71.2$ kilograms.

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is

$50 \times 35 \times 6 = 10,500$ cubic feet.

One cubic foot is equal to (about) 7.5 gallons.

The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?

Which is the greater quantity?

(a) The sidelength of a cube with surface area $600 \textrm{ cm}^{2}$

(b) The sidelength of a cube with volume $1,000 \textrm{ cm}^{3}$

Which is the greater quantity?

(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters

(b) The volume of a cube with sidelength 300 millimeters

Use the volume formula, substituting :

$V=22 \cdot 12 \cdot 12 = 3168^{3}$

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the volume formula, substituting :

$V = 90 \cdot 60 \cdot 60 = 324,000$ cubic centimeters

The volume of the cube is $20 ^{3} = 20 \times 20 \times 20 = 8,000$ cubic centimeters. Multiply by the number of grams per cubic centimeter to get $8,000 \times 8.9 = 71,200$ grams, or $71,200 \div 1,000 = 71.2$ kilograms.

The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is

$50 \times 35 \times 6 = 10,500$ cubic feet.

One cubic foot is equal to (about) 7.5 gallons.

The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?

Which is the greater quantity?

(a) The sidelength of a cube with surface area $600 \textrm{ cm}^{2}$

(b) The sidelength of a cube with volume $1,000 \textrm{ cm}^{3}$

Which is the greater quantity?

(a) The volume of a rectangular prism with length 60 centimeters, width 30 centimeters, and height 15 centimeters

(b) The volume of a cube with sidelength 300 millimeters

Use the volume formula, substituting :

$V=22 \cdot 12 \cdot 12 = 3168^{3}$

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

$0.9 \times 100 = 90$ centimeters

$0.6 \times 100 = 60$ centimeters

Use the volume formula, substituting :

$V = 90 \cdot 60 \cdot 60 = 324,000$ cubic centimeters