### All SAT II Math II Resources

## Example Questions

### Example Question #11 : Volume

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

**Possible Answers:**

**Correct answer:**

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:**

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:**

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:**

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:**

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:**

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:**

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:**

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:**

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:**

Write the formula for the sphere.

Substitute the radius.

The answer is: