SAT II Math I : Volume

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

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Example Question #1 : 3 Dimensional Geometry

A circular swimming pool has diameter  meters and depth 2 meters throughout. Which of the following expressions give the amount of water it holds, in cubic meters?

Possible Answers:

Correct answer:

Explanation:

The pool can be seen as a cylinder with diameter  - and, subsequently, radius half this, or  - and depth, or height, 2. The volume of a cylinder is defined by the formula

Example Question #2 : 3 Dimensional Geometry

Swimming_pool

The above depicts a rectangular swimming pool for an apartment. 60% of the pool is six feet deep, and the remaining part of the pool is four feet deep. How many cubic feet of water does the pool hold?

Possible Answers:

None of the other choices gives the correct answer.

Correct answer:

None of the other choices gives the correct answer.

Explanation:

The cross-section of the pool is the area of its surface, which is the product of its length and its width:

 square feet.

Since 60% of the pool is six feet deep, this portion of the pool holds 

 cubic feet of water.

Since the remainder of the pool - 40% - is four feet deep, this portion of the pool holds 

 cubic feet of water.

Add them together: the pool holds 

 cubic feet of water.

This answer is not among the choices.

Example Question #3 : 3 Dimensional Geometry

Find the volume of a cube in inches with a side of 

Possible Answers:

Correct answer:

Explanation:

Convert the side dimension to inches first before finding the volume.

Write the volume for a cube and substitute the new side to obtain the volume in inches.

Example Question #4 : 3 Dimensional Geometry

Example cylinder

Figure not drawn to scale.

What is the volume of the cylinder above?

Possible Answers:

56.55 in3

52.36 in3

48.79 in3

94.25 in3

66.13 in3

Correct answer:

56.55 in3

Explanation:

In order to find the volume of a cylinder, you find the area of the circular top and multiply it by the height.

Example cylinder

The volume of the cylinder is 56.55 in3

Example Question #5 : 3 Dimensional Geometry

Cone example

Figure not drawn to scale

If the volume of the cone above is 47.12 ft3, what is the radius of the base?

Possible Answers:

3.5ft

4 ft

5 ft

2 ft

3 ft

Correct answer:

3 ft

Explanation:

Because we have been given the volume of the cone and have been asked to find the radius of the base of the cone, we must work backwards using the volume formula.

Cone example

The radius of the base of the cone is 3 ft.

Example Question #6 : 3 Dimensional Geometry

Box example

Figure not drawn to scale.

What is the volume of the above image?

Possible Answers:

64 yd3

42 yd2

42 yd3

32 yd3

84 yd2

Correct answer:

42 yd3

Explanation:

Box example
You can find the volume of a box by following the equation below:

The surface area of the box is 42 yd(remember that volume measurements are cubic units NOT square units)

Example Question #1 : Volume

What is the volume of the following tetrahedron? Assume the figure is a regular tetrahedron.

Tetrahedron

Possible Answers:

Correct answer:

Explanation:

A regular tetrahedron is composed of four equilateral triangles. The formula for the volume of a regular tetrahedron is:

, where  represents the length of the side.

Plugging in our values we get:

Example Question #8 : 3 Dimensional Geometry

Find the volume of a tetrahedron with an edge of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a tetrahedron.

Substitute in the length of the edge provided in the problem.

Rationalize the denominator.

Example Question #2 : Volume

Find the volume of a tetrahedron with an edge of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a tetrahedron.

Substitute in the length of the edge provided in the problem:

Cancel out the  in the denominator with one in the numerator:

A square root is being raised to the power of two in the numerator; these two operations cancel each other out. After canceling those operations, reduce the remaining fraction to arrive at the correct answer:

Example Question #10 : 3 Dimensional Geometry

Find the volume of a tetrahedron with an edge of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for finding the volume of a tetrahedron.

Substitute in the edge length provided in the problem. 

Cancel out the  in the denominator with part of the  in the numerator:

Expand, rationalize the denominator, and reduce to arrive at the correct answer:

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