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Intermediate Geometry : How to find the volume of a prism

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Example Questions

Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

A prism with a square base has a height of $\displaystyle 4$ feet.

If the edge of the base is $\displaystyle 2$ feet, what is the volume of the prism?

Possible Answers:

$4\, ft^3$ $\displaystyle 4\, ft^3$

$6\, ft^3$ $\displaystyle 6\, ft^3$

$8\, ft^3$ $\displaystyle 8\, ft^3$

$16\, ft^3$ $\displaystyle 16\, ft^3$

Correct answer:

$16\, ft^3$ $\displaystyle 16\, ft^3$

Explanation:

The volume of a prism is given as

V = Bh $\displaystyle V = Bh$

where

B = Area of the base

and

h = height of the prism.

Because the base is a square, we have

$\displaystyle B = s^2 = 2^2 = 4$

So plugging in the value of B that we found and h that was given in the problem we get the volume to be the following.

$V = 4\cdot4 = 16\,ft^3$ $\displaystyle V = 4\cdot4 = 16\,ft^3$

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Example Question #1 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

A rectangular prism has the dimensions of $2\:in$ $\displaystyle 2\:in$, $5\:in$ $\displaystyle 5\:in$, and $7\:in$ $\displaystyle 7\:in$. What is the volume of the prism?

Possible Answers:

$70\:in^3$ $\displaystyle 70\:in^3$

$63\: in^3$ $\displaystyle 63\: in^3$

$70\:in^2$ $\displaystyle 70\:in^2$

$72\:in^3$ $\displaystyle 72\:in^3$

$63 \:in^2$ $\displaystyle 63 \:in^2$

Correct answer:

$70\:in^3$ $\displaystyle 70\:in^3$

Explanation:

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$ $\displaystyle V= l \cdot w \cdot h$

In this equation, $\displaystyle l$ is length, $\displaystyle w$ is width, and $\displaystyle h$ is height.

The given information does not explicitly state which side each dimension measurement correlates to on the prism. Volume simply requires the multiplication of the dimensions together.

Volume can be solved for in the following way:

$V = 2\:in \cdot 5\:in \cdot 7\:in$ $\displaystyle V = 2\:in \cdot 5\:in \cdot 7\:in$

$V = 10\:in^2 \cdot 7\:in$ $\displaystyle V = 10\:in^2 \cdot 7\:in$

$V= 70 \:in^3$ $\displaystyle V= 70 \:in^3$

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Example Question #2 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Find the volume of a rectangular prism with a width of $2\:cm$ $\displaystyle 2\:cm$, height of $8\:cm$ $\displaystyle 8\:cm$ and length of $3\:cm$ $\displaystyle 3\:cm$.

Possible Answers:

$58\:cm^3$ $\displaystyle 58\:cm^3$

$24\:cm^3$ $\displaystyle 24\:cm^3$

$48\:cm^3$ $\displaystyle 48\:cm^3$

$56\:cm^3$ $\displaystyle 56\:cm^3$

$26\:cm^3$ $\displaystyle 26\:cm^3$

Correct answer:

$48\:cm^3$ $\displaystyle 48\:cm^3$

Explanation:

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$ $\displaystyle V= l \cdot w \cdot h$

In this equation, $\displaystyle l$ is length, $\displaystyle w$ is width, and $\displaystyle h$ is height.

Because all the necessary information has been provided to solve for the volume, all that needs to be done is substituting in the values for the variables.

Therefore:

$V = 2\:cm \cdot 3\:cm \cdot 8\:cm$ $\displaystyle V = 2\:cm \cdot 3\:cm \cdot 8\:cm$

$V = 6\:cm^2 \cdot 8\:cm$ $\displaystyle V = 6\:cm^2 \cdot 8\:cm$

$V = 48\:cm^3$ $\displaystyle V = 48\:cm^3$

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Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Find the surface area of the rectangular prism:

Volume_of_a_prism

Possible Answers:

$418\:units^3$ $\displaystyle 418\:units^3$

$453\:units^3$ $\displaystyle 453\:units^3$

$468\:units^3$ $\displaystyle 468\:units^3$

$410\:units^2$ $\displaystyle 410\:units^2$

$468\:units^2$ $\displaystyle 468\:units^2$

Correct answer:

$410\:units^2$ $\displaystyle 410\:units^2$

Explanation:

The surface area of a rectangular prism is

$\displaystyle SA=2lw+2lh+2wh$

Substituting in the given information for this particular rectangular prism.

$\\SA=2(13\cdot 9)+2(13\cdot 4)+2(9\cdot 4) \\SA=410\ \text{units}^2$ $\displaystyle \\SA=2(13\cdot 9)+2(13\cdot 4)+2(9\cdot 4) \\SA=410\ \text{units}^2$

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Example Question #4 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

A small rectangular fish tank has sides that are 18in $\displaystyle 18in$ wide, 30in $\displaystyle 30in$ long, and 24in $\displaystyle 24in$ high. Which formula would not work to find the correct volume of the fish tank?

Possible Answers:

$720 \times 18$ $\displaystyle 720 \times 18$

$(18 \times 30) + 24$ $\displaystyle (18 \times 30) + 24$

$30 \times 432$ $\displaystyle 30 \times 432$

$(30 \times 24) \times 18$ $\displaystyle (30 \times 24) \times 18$

$(24 \times 18) \times 30$ $\displaystyle (24 \times 18) \times 30$

Correct answer:

$(18 \times 30) + 24$ $\displaystyle (18 \times 30) + 24$

Explanation:

In this question the formula that uses addition will not yield the correct volume of the fish tank:

$\displaystyle (18 x 30) + 24$

This is the correct answer because in order to find the volume of any rectangular prism one needs to multiply the prism's length, width, and height together.

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$ $\displaystyle V= l \cdot w \cdot h$

In this equation, $\displaystyle l$ is length, $\displaystyle w$ is width, and $\displaystyle h$ is height.

To restate, $\displaystyle (18 x 30) + 24$ is the correct answer because it will NOT yield the correct volume, you would need to multiply $\displaystyle 24$ by the product of $\displaystyle 18$ and $\displaystyle 30$, not add.

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

Find the volume of the prism.

Possible Answers:

1880 $\displaystyle 1880$

1720 $\displaystyle 1720$

1800 $\displaystyle 1800$

1960 $\displaystyle 1960$

Correct answer:

1800 $\displaystyle 1800$

Explanation:

Recall how to find the volume of a prism:

$\text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$ $\displaystyle \text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(12)(15)=90$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(12)(15)=90$

Now, find the volume of the prism.

$\text{Volume of Prism}=90 \times 20 =1800$ $\displaystyle \text{Volume of Prism}=90 \times 20 =1800$

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Example Question #5 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

450 $\displaystyle 450$

360 $\displaystyle 360$

540 $\displaystyle 540$

270 $\displaystyle 270$

Correct answer:

270 $\displaystyle 270$

Explanation:

Recall how to find the volume of a prism:

$\text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$ $\displaystyle \text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(3)(9)=13.5$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(3)(9)=13.5$

Now, find the volume of the prism.

$\text{Volume of Prism}=13.5\times 20 =270$ $\displaystyle \text{Volume of Prism}=13.5\times 20 =270$

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Example Question #161 : Solid Geometry

Find the volume of the prism.

Possible Answers:

335 $\displaystyle 335$

305 $\displaystyle 305$

325 $\displaystyle 325$

315 $\displaystyle 315$

Correct answer:

315 $\displaystyle 315$

Explanation:

Recall how to find the volume of a prism:

$\text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$ $\displaystyle \text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(5)(9)=22.5$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(5)(9)=22.5$

Now, find the volume of the prism.

$\text{Volume of Prism}=22.5\times 14=315$ $\displaystyle \text{Volume of Prism}=22.5\times 14=315$

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Example Question #8 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

696 $\displaystyle 696$

690 $\displaystyle 690$

684 $\displaystyle 684$

678 $\displaystyle 678$

Correct answer:

684 $\displaystyle 684$

Explanation:

Recall how to find the volume of a prism:

$\text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$ $\displaystyle \text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(6)(12)=36$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(6)(12)=36$

Now, find the volume of the prism.

$\text{Volume of Prism}=36\times 19=684$ $\displaystyle \text{Volume of Prism}=36\times 19=684$

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

Find the volume of a prism.

Possible Answers:

450 $\displaystyle 450$

690 $\displaystyle 690$

580 $\displaystyle 580$

510 $\displaystyle 510$

Correct answer:

510 $\displaystyle 510$

Explanation:

Recall how to find the volume of a prism:

$\text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$ $\displaystyle \text{Volume of Prism}=\text{Area of base}\times\text{height of prism}$

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(5)(12)=30$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(5)(12)=30$

Now, find the volume of the prism.

$\text{Volume of Prism}=30\times 17=510$ $\displaystyle \text{Volume of Prism}=30\times 17=510$

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Intermediate Geometry : How to find the volume of a prism

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #1 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #2 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #4 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

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

Example Question #5 : How To Find The Volume Of A Prism

Example Question #161 : Solid Geometry

Example Question #8 : How To Find The Volume Of A Prism

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

All Intermediate Geometry Resources

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