### All GRE Math Resources

## Example Questions

### Example Question #341 : Geometry

Find the surface area of a sphere with a diameter of 14. Use *π* = 22/7.

**Possible Answers:**

2464

616

1256

428

872

**Correct answer:**

616

Surface Area = 4*πr*^{2} = 4 * 22/7 * 7^{2} = 616

### Example Question #342 : Geometry

A sphere has a surface area of square inches. If the radius is doubled, what is the surface area of the larger sphere?

**Possible Answers:**

Cannot be determined

**Correct answer:**

The surface area of the larger sphere is NOT merely doubled from the smaller sphere, so we cannot double to find the answer.

We can use the surface area formula to find the radius of the original sphere.

*r*^{2} = 4

*r* = 2

Therefore the larger sphere has a radius of 2 * 2 = 4.

The new surface area is then square inches.

### Example Question #3 : How To Find The Surface Area Of A Sphere

If a sphere has a volume of cubic inches, what is its surface area?

**Possible Answers:**

**Correct answer:**

The volume of a cube is equal to .

So we mutiply our volume by and divide by , giving us .

The surface area of a sphere is equal to , giving us .

### Example Question #343 : Geometry

How much does the volume of a sphere increase if its radius is increased by 50%?

**Possible Answers:**

237.5%

150%

50%

0.3375%

337.5%

**Correct answer:**

237.5%

Recall the equation for the volume of a sphere:

V = (4/3)πr^{3}

If we increase the radius by 50%, we can represent the new radius as being equal to r + 0.5r = 1.5r.

Replace this into the equation for the volume and simplify:

V_{2} = (4/3)π(1.5r)^{3} = (4/3)π(3.375r^{3})

Rewrite this so that you can compare the two volumes:

V_{2 }= 3.375 * (4/3)πr^{3} = 3.375 * [(4/3)πr^{3}]

This is the same as:

V_{2} = 3.375 * V

This means that the new volume is 337.5% of the original. However, note that the question asked for the increase, which would be an increase by 237.5%.

### Example Question #344 : Geometry

A cube weighs 216 grams. If you carve a sphere out of the cube such that the diameter of the sphere is equal to one of the sides of the square, how many grams is the weight of the resulting sphere?

**Possible Answers:**

9π

216π

144π

36π

288π

**Correct answer:**

36π

Remember that the weight of an object is analogous to the volume. Since the weight of the sphere is 216, the volume of the sphere is proportional to 216. Remember the equation for volume of a sphere:

V = a * a * a = 216

Take the cube root of 216 to find that the length of one of the cubes is proportional to 6. According to the question, one of the sides of the cube is equivalent to the diameter of the sphere.

Thus d = 6 and r = d/2 = 3 for the sphere.

Remember the volume equation for a sphere:

V = 4/3 * π * r^{3}

Plug in r = 3 to find V = 36π

### Example Question #345 : Geometry

What is the volume of a sphere with a radius of 3?

**Possible Answers:**

36*π*

48*π*

112*π*

24*π*

96*π*

**Correct answer:**

36*π*

Volume of a sphere = 4/3 * *πr*^{3} = 4/3 * *π* * 3^{3 }= 36*π*

### Example Question #346 : Geometry

How many times greater is the volume of a sphere with radius of 3 than the volume of a sphere with radius of ?

**Possible Answers:**

**Correct answer:**

The formula for the volume of a sphere is .

Use this to find the volume of each sphere, then take the quotient of the two volumes to determine the relationship between the two.

For the first sphere, .

For the second sphere, .

Since both volumes have factors of 4/3 and pi, we'll ignore those and divide by the remaining factors. Keep in mind that the volume of the first sphere must be in the numerator due to the wording of the question.

### Example Question #345 : Geometry

If a sphere has a volume of cubic inches, what is the approximate radius of the sphere?

**Possible Answers:**

**Correct answer:**

The formula for the volume of a sphere is

where is the radius of the sphere.

Therefore,

, giving us .

### Example Question #2 : How To Find The Radius Of A Sphere

A rectangular prism has the dimensions . What is the volume of the largest possible sphere that could fit within this solid?

**Possible Answers:**

**Correct answer:**

For a sphere to fit into the rectangular prism, its dimensions are constrained by the prism's smallest side, which forms its diameter. Therefore, the largest sphere will have a diameter of , and a radius of .

The volume of a sphere is given as:

And thus the volume of the largest possible sphere to fit into this prism is

### Example Question #347 : Geometry

What is the radius of a sphere with volume cubed units?

**Possible Answers:**

**Correct answer:**

The volume of a sphere is represented by the equation . Set this equation equal to the volume given and solve for r:

Therefore, the radius of the sphere is 3.