SAT II Math II : 3-Dimensional Geometry

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

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Example Questions

Example Question #11 : Volume

Find the volume of a sphere with a diameter of 10.

Possible Answers:

Correct answer:

Explanation:

The surface area of a sphere is found using the formula . We are given the diameter of the circle and so we have to use it to find the radius (r).

Plug r into the formula to find the surface area

Example Question #391 : Sat Subject Test In Math Ii

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

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a cube.

Substitute the length into the formula.

The volume is:  

Example Question #11 : Volume

Billy has a ice cream cone that consists of a cone and hemisphere.  Suppose the cone has a height of 4 inches, and the radius of the hemisphere is 2 inches.  Assuming that the combined shape is not irregular, what is the total volume?

Possible Answers:

Correct answer:

Explanation:

Write the volume for a cone.

Substitute the radius and height.  The radius is 2.

Write the volume for a hemisphere.  This should be half the volume of the full sphere.

Substitute the radius.

Add the volumes of the cone and hemisphere to determine the total volume.

The answer is:  

Example Question #11 : 3 Dimensional Geometry

Find the volume of a sphere with a diameter of .

Possible Answers:

Correct answer:

Explanation:

Divide the diameter by two to get the radius.  This is also the same as multiplying the diameter by one-half.

Write the formula for the volume of the sphere.

Substitute the radius.

Simplify the terms.

The answer is:  

Example Question #91 : Geometry

If the side of a cube is , what must be the volume?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a cube.

Substitute the side length.  When we are multiplying common bases with exponents, we are adding the exponents instead.

The answer is:  

Example Question #11 : 3 Dimensional Geometry

Determine the volume of a cube if the side length is .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the volume of a cube.

Substitute the side length into the equation.

The answer is:  

Example Question #11 : 3 Dimensional Geometry

The radius and the height of a cylinder are equal. If the volume of the cylinder is , what is the diameter of the cylinder?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the volume of a cylinder:

Since we know that the radius and the height are equal, we can rewrite the equation:

Using the given volume, find the length of the radius.

Since the question asks you to find the diameter, multiply the radius by two.

 

Example Question #391 : Sat Subject Test In Math Ii

Determine the volume of the cube if the side lengths are .

Possible Answers:

Correct answer:

Explanation:

The volume of a cube is:  

Substitute the dimensions.

The answer is:  

Example Question #11 : Volume

Determine the volume of a sphere with a diameter of 6.

Possible Answers:

Correct answer:

Explanation:

The radius is half the diameter, which is three.

Write the formula for the volume of a sphere.

Substitute the radius.

The answer is:  

Example Question #11 : 3 Dimensional Geometry

Find the volume of a sphere with a radius of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the sphere.

Substitute the radius.

The answer is:  

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