How to find the volume of a prism

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Math › How to find the volume of a prism

Questions 1 - 5

1

Find the volume of the following triangular prism:

Triangular_prism

$108\sqrt{3}m^3$

$98\sqrt{3}m^3$

$88\sqrt{3}m^3$

$118\sqrt{3}m^3$

$128\sqrt{3}m^3$

Explanation

The formula for the volume of an equilateral, triangular prism is:

$V = \left(\frac{s^2\sqrt{3}}{4}\right)(h)$

Where is the length of the triangle side and is the length of the height.

Plugging in our values, we get:

$V = \left(\frac{(6m)^2\sqrt{3}}{4}\right)(12m)$

$V=108\sqrt{3}m^3$

2

Find the volume of the following triangular prism.

Half_box

Explanation

The formula for the volume of a triangular prism is:

$V = \frac{1}{2} (l)(w)(h)$

Where is the length of the triangle, is the width of the triangle, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2} (6m)(6m)(9m)$

3

Find the volume of the following triangular prism.

Half_box

Explanation

The formula for the volume of a triangular prism is:

$V = \frac{1}{2}(l)(w)(h)$

Where is the length of the base, is the width of the base, and is the height of the prism

Plugging in our values, we get:

$V = \frac{1}{2}(8m)(8m)(12m)$

4

A rectangular box has two sides with the following lengths:

and

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

12

16

21

28

49

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.

$84=3\times 4\times x$

Divide both sides of the equation by 12.

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

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.

$A=l\times w$

$A=4\times 7$

5

What is the volume?

Question_5

Explanation

The volume is calculated using the equation:

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