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Intermediate Geometry : How to find the volume of a prism

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Example Question #61 : Geometry

A prism with a square base has a height of feet.

If the edge of the base is feet, what is the volume of the prism?

Possible Answers:

$8\, ft^3$

$16\, ft^3$

$6\, ft^3$

$4\, ft^3$

Correct answer:

$16\, ft^3$

Explanation:

The volume of a prism is given as

V = Bh

where

B = Area of the base

and

h = height of the prism.

Because the base is a square, we have

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.

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

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

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

Possible Answers:

$70\:in^2$

$72\:in^3$

$63\: in^3$

$63 \:in^2$

$70\:in^3$

Correct answer:

$70\:in^3$

Explanation:

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

$V= l \cdot w \cdot h$

In this equation, is length, is width, and 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:

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

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

$V= 70 \:in^3$

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Example Question #5 : 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 $2\:cm$ , height of $8\:cm$ and length of $3\:cm$ .

Possible Answers:

$48\:cm^3$

$26\:cm^3$

$58\:cm^3$

$24\:cm^3$

$56\:cm^3$

Correct answer:

$48\:cm^3$

Explanation:

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

$V= l \cdot w \cdot h$

In this equation, is length, is width, and 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:

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

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

$V = 48\:cm^3$

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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 surface area of the rectangular prism:

Volume_of_a_prism

Possible Answers:

$468\:units^3$

$453\:units^3$

$410\:units^2$

$468\:units^2$

$418\:units^3$

Correct answer:

$410\:units^2$

Explanation:

The surface area of a rectangular prism is

SA=2lw+2lh+2wh

Substituting in the given information for this particular rectangular prism.

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

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

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

Possible Answers:

$(30 \times 24) \times 18$

$(18 \times 30) + 24$

$720 \times 18$

$(24 \times 18) \times 30$

$30 \times 432$

Correct answer:

$(18 \times 30) + 24$

Explanation:

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

(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:

$V= l \cdot w \cdot h$

In this equation, is length, is width, and is height.

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

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Example Question #21 : Prisms

Find the volume of the prism.

Possible Answers:

1800

1960

1720

1880

Correct answer:

1800

Explanation:

Recall how to find the volume of a prism:

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

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

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

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

Now, find the volume of the prism.

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

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

Find the volume of the prism.

Possible Answers:

270

360

450

540

Correct answer:

270

Explanation:

Recall how to find the volume of a prism:

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

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

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

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

Now, find the volume of the prism.

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

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Example Question #2 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

335

325

315

305

Correct answer:

315

Explanation:

Recall how to find the volume of a prism:

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

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

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

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

Now, find the volume of the prism.

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

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

Find the volume of the prism.

Possible Answers:

696

678

690

684

Correct answer:

684

Explanation:

Recall how to find the volume of a prism:

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

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

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

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

Now, find the volume of the prism.

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

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Example Question #4 : How To Find The Volume Of A Prism

Find the volume of a prism.

Possible Answers:

690

510

580

450

Correct answer:

510

Explanation:

Recall how to find the volume of a prism:

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

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

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

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

Now, find the volume of the prism.

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

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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 #61 : Geometry

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

Example Question #5 : 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 #1 : How To Find The Volume Of A Prism

Example Question #21 : Prisms

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

Example Question #2 : How To Find The Volume Of A Prism

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

Example Question #4 : How To Find The Volume Of A Prism

All Intermediate Geometry Resources

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