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Intermediate Geometry : How to find the volume of a prism

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Example Question #228 : Solid Geometry

Pyramid

The above figure shows a square pyramid inscribed inside a cube. The pyramid has volume 100. Give the volume of the cube.

Possible Answers:

250

200

$233\frac{1}{3}$

$333\frac{1}{3}$

300

Correct answer:

300

Explanation:

Let be the length of one side of the cube. Then the base of the pyramid is a square with sidelength , and its area is

$B = s^{2}$ .

The volume of a pyramid is one third the product of its height and the area of its base. The height of the pyramid is , so the volume is

$V_{1} = \frac{1}{3} Bh = \frac{1}{3} s^{2} \cdot s = \frac{1}{3} s^{3}$

The volume of the cube is $V_{2} = s^{3}$ , so

$V_{1} = \frac{1}{3} V_{2}$

or, equivalently,

$3 \cdot V_{1} =3 \cdot \frac{1}{3} V_{2}$

$V_{2} = 3 \cdot V_{1}$

That is, the volume of the cube is three times that of the pyramid, and, since the pyramid has volume 100, the volume of the cube is $3 \cdot 100 =300$ .

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

A rectangular box has two sides with the following lengths:

3$ cm$ and 4 $ cm$

If it possesses a volume of $84$ cm$^{3}$ , what is the area of its largest side?

Possible Answers:

Correct answer:

Explanation:

The volume of a rectangular prism is found using the following formula:

$V=l\times w\times h$

If we substitute our known values, then we can solve for the missing side.

$84=3\times 4\times x$

84=12x

Divide both sides of the equation by 12.

$\frac{84}{12}=\frac{12x}{12}$

x=7

We now know that the missing length equals 7 centimeters.

This means that the box can have sides with the following dimensions: 3cm by 4cm; 7cm by 3cm; or 7cm by 4cm. The greatest area of one side belongs to the one that is 7cm by 4cm.

$A=l\times w$

$A=4\times 7$

A=28

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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 #228 : Solid Geometry

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

All Intermediate Geometry Resources

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