Volume of a Three-Dimensional Figure

Help Questions

SSAT Upper Level Quantitative › Volume of a Three-Dimensional Figure

Questions 1 - 10

1

Find the volume of a cube with a side length of .

$8\textup{,}000$

$4\textup{,}000$

$6\textup{,}000$

Explanation

Write the formula for the volume of a cube.

$V=a^3=(20)^3=8\textup{,}000$

The correct answer is $8\textup{,}000$ .

2

Box

The above diagram shows a rectangular solid. The shaded side is a square. Give the volume of the solid.

Explanation

A square has four sides of equal length, so, as seen in the diagram below, the length, width, and height of the solid are 20, 10, and 10.

Box 3

The volume of the solid is the product of the three dimensions:

$V = LWH = 20 \cdot 10 \cdot 10 = 2,000$ .

3

Box

The above diagram shows a rectangular solid. The shaded side is a square. Give the volume of the solid.

Explanation

A square has four sides of equal length, so, as seen in the diagram below, the length, width, and height of the solid are 20, 10, and 10.

Box 3

The volume of the solid is the product of the three dimensions:

$V = LWH = 20 \cdot 10 \cdot 10 = 2,000$ .

4

Find the volume of a regular tetrahedron that has a side length of .

$\frac{16\sqrt2}{3}$

$32\sqrt2$

$\frac{64}{3\sqrt2}$

$\frac{8\sqrt2}{3}$

Explanation

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}4^3$

$\text{Volume}=\frac{64\sqrt2}{12}$

$\text{Volume}=\frac{16\sqrt2}{3}$

5

Find the volume of a prism that has a right triangle base with leg lengths of and and a height of .

Explanation

To find the volume of a prism, multiply the area of the base by the height.

$\text{Area of Base}=\frac{3\times8}{2}=12$

$\text{Volume}=12\times height=12\times12=144$

6

Find the volume of a cube with a side length of .

$8\textup{,}000$

$4\textup{,}000$

$6\textup{,}000$

Explanation

Write the formula for the volume of a cube.

$V=a^3=(20)^3=8\textup{,}000$

The correct answer is $8\textup{,}000$ .

7

Find the volume of a prism that has a right triangle base with leg lengths of and and a height of .

Explanation

To find the volume of a prism, multiply the area of the base by the height.

$\text{Area of Base}=\frac{3\times8}{2}=12$

$\text{Volume}=12\times height=12\times12=144$

8

Find the volume of a regular tetrahedron that has a side length of .

$\frac{16\sqrt2}{3}$

$32\sqrt2$

$\frac{64}{3\sqrt2}$

$\frac{8\sqrt2}{3}$

Explanation

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}4^3$

$\text{Volume}=\frac{64\sqrt2}{12}$

$\text{Volume}=\frac{16\sqrt2}{3}$

9

Find the volume of a regular tetrahedron that has a side length of .

$\frac{125\sqrt2}{12}$

$\frac{25\sqrt2}{12}$

$20\sqrt2$

$\frac{5\sqrt2}{6}$

Explanation

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}5^3$

$\text{Volume}=\frac{125\sqrt2}{12}$

10

Find the volume of a regular tetrahedron that has a side length of .

$\frac{125\sqrt2}{12}$

$\frac{25\sqrt2}{12}$

$20\sqrt2$

$\frac{5\sqrt2}{6}$

Explanation

Use the following formula to find the volume of a regular tetrahedron:

$\text{Volume}=\frac{\sqrt2}{12}side^3$

Now, plug in the given side length.

$\text{Volume}=\frac{\sqrt2}{12}5^3$

$\text{Volume}=\frac{125\sqrt2}{12}$

Page 1 of 24

Return to subject

AI TutorYour personal study buddy

Question of the DayDaily practice to build your skills

FlashcardsStudy and memorize key concepts

WorksheetsBuild custom practice quizzes

AI SolverStep-by-step problem solutions

Learn by ConceptMaster concepts step by step

Diagnostic TestsAssess your knowledge level

Practice TestsTest your skills with exam questions

GamesLearn through free games