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ISEE Middle Level Math : Solid Geometry

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Example Questions

Example Question #151 : Geometry

Prism

Give the volume of the above box in cubic centimeters.

Possible Answers:

$21,600\textrm{ cm}^{3}$

$32,400 \textrm{ cm}^{3}$

$216,000 \textrm{ cm}^{3}$

$28,800 \textrm{ cm}^{3}$

$324,000 \textrm{ cm}^{3}$

Correct answer:

$324,000 \textrm{ cm}^{3}$

Explanation:

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 L = 90, W = H = 60 :

V = LWH

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

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Example Question #152 : Geometry

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?

Possible Answers:

$71.2 \textrm{ kg}$

$35.6 \textrm{ kg}$

$7.12 \textrm{ kg}$

$3.56 \textrm{ kg}$

Correct answer:

$71.2 \textrm{ kg}$

Explanation:

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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Example Question #1 : How To Find The Volume Of A Net

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

Possible Answers:

$4 \frac{1}{4} \textrm{ ft}^{3}$

$3 \frac{3}{4} \textrm{ ft}^{3}$

$4 \frac{3}{4} \textrm{ ft}^{3}$

$4 \frac{1}{2} \textrm{ ft}^{3}$

Correct answer:

$3 \frac{3}{4} \textrm{ ft}^{3}$

Explanation:

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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Example Question #153 : Geometry

Prism

Give the volume of the box in cubic inches.

Possible Answers:

$3,168 \textrm{ in}^{3}$

$1,344 \textrm{ in}^{3}$

$1,056 \textrm{ in}^{3}$

$672 \textrm{ in}^{3}$

$816 \textrm{ in}^{3}$

Correct answer:

$3,168 \textrm{ in}^{3}$

Explanation:

Use the volume formula, substituting L = 22, W = H = 12 :

V=LWH

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

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Example Question #1 : Nets

Swimming_pool

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?

Possible Answers:

$8,925 \textrm{ gal}$

$17,850 \textrm{ gal}$

$178,500 \textrm{ gal}$

$91,875 \textrm{ gal}$

$89,250 \textrm{ gal}$

Correct answer:

$91,875 \textrm{ gal}$

Explanation:

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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Example Question #2 : Nets

Swimming_pool

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?

Possible Answers:

$9,500\textrm{ ft}^{3}$

$51,000\textrm{ ft}^{3}$

$510\textrm{ ft}^{3}$

$1,020\textrm{ ft}^{3}$

$10,500\textrm{ ft}^{3}$

Correct answer:

$10,500\textrm{ ft}^{3}$

Explanation:

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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ISEE Middle Level Math : Solid Geometry

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #151 : Geometry

Example Question #152 : Geometry

Example Question #1 : How To Find The Volume Of A Net

Example Question #153 : Geometry

Example Question #1 : Nets

Example Question #2 : Nets

All ISEE Middle Level Math Resources

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