### All High School Math Resources

## Example Questions

### Example Question #131 : Solid Geometry

The radius of a sphere is . What is the approximate volume of this sphere?

**Possible Answers:**

**Correct answer:**

### Example Question #132 : Solid Geometry

A cube has a side dimension of 4. A sphere has a radius of 3. What is the volume of the two combined, if the cube is balanced on top of the sphere?

**Possible Answers:**

**Correct answer:**

### Example Question #133 : Solid Geometry

What is the volume of a sphere with a diameter of 6 in?

**Possible Answers:**

**Correct answer:**

The formula for the volume of a sphere is:

where = radius. The diameter is 6 in, so the radius will be 3 in.

### Example Question #134 : Solid Geometry

A solid hemisphere has a radius of length *r*. Let *S* be the number of square units, in terms of *r*, of the hemisphere's surface area. Let *V* be the number of cubic units, in terms of *r*, of the hemisphere's volume. What is the ratio of *S* to *V*?

**Possible Answers:**

**Correct answer:**

First, let's find the surface area of the hemisphere. Because the hemisphere is basically a full sphere cut in half, we need to find half of the surface area of a full sphere. However, because the hemisphere also has a circular base, we must then add the area of the base.

(surface area of sphere) + (surface area of base)

The surface area of a sphere with radius *r* is equal to . The surface area of the base is just equal to the surface area of a circle, which is .

The volume of the hemisphere is going to be half of the volume of an entire sphere. The volume for a full sphere is .

(volume of sphere)

Ultimately, the question asks us to find the ratio of *S* to *V*. To do this, we can write *S* to *V* as a fraction.

In order to simplify this, let's multiply the numerator and denominator both by 3.

=

The answer is .

### Example Question #1 : How To Find The Volume Of A Sphere

If the diameter of a sphere is , find the approximate volume of the sphere?

**Possible Answers:**

**Correct answer:**

The volume of a sphere =

Radius is of the diameter so the radius = 5.

or

which is approximately

### Example Question #1 : How To Find The Surface Area Of A Sphere

What is the surface area of a sphere with a radius of 15?

**Possible Answers:**

**Correct answer:**

To solve for the surface area of a sphere you must use the equation

First, plug in 15 for and square it

Multiply by 4 and to get

The answer is .

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

What is the surface area of a sphere whise radius is .

**Possible Answers:**

Not enough information to solve

**Correct answer:**

The surface area of a sphere is found by the formula using the given radius of .

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

Find the surface area of a sphere whose diameter is .

**Possible Answers:**

**Correct answer:**

The surface area of a sphere is found by the formula . We need to first convert the given diameter of to the sphere's radius.

Now, we can solve for surface area.

### Example Question #4 : How To Find The Surface Area Of A Sphere

To the nearest tenth of a square centimeter, give the surface area of a sphere with volume 1,000 cubic centimeters.

**Possible Answers:**

**Correct answer:**

The volume of a sphere in terms of its radius is

Substitute and solve for :

Substitute for in the formula for the surface area of a sphere:

### Example Question #5 : How To Find The Surface Area Of A Sphere

Find the surface area of a sphere with a radius of .

**Possible Answers:**

**Correct answer:**

The standard equation to find the area of a sphere is .

Substitute the given radius into the standard equation to get the answer:

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