High School Math : Spheres

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #131 : Solid Geometry

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

Possible Answers:

20\pi

288\pi

516\pi

138\pi

300\pi

Correct answer:

288\pi

Explanation:

Volume=\frac{4}{3}\pi r^{3}

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:

Explanation:

Example Question #133 : Solid Geometry

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

Possible Answers:

Correct answer:

Explanation:

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:

\frac{4r}{3}

\frac{9r}{2}

\frac{3}{r}

3r

\frac{9}{2r}

Correct answer:

\frac{9}{2r}

Explanation:

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.

S = \frac{1}{2}\cdot (surface area of sphere) + (surface area of base)

The surface area of a sphere with radius r is equal to 4\pi r^2. The surface area of the base is just equal to the surface area of a circle, which is \pi r^2.

S=\frac{1}{2}\cdot 4\pi r^2+\pi r^2=2\pi r^2+\pi r^2=3\pi r^2

The volume of the hemisphere is going to be half of the volume of an entire sphere. The volume for a full sphere is \frac{4}{3}\pi r^3.

V = \frac{1}{2}\cdot (volume of sphere)

V = \frac{1}{2}\cdot \frac{4}{3}\pi r^3=\frac{2}{3}\pi r^3

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.

\frac{S}{V}=\frac{3\pi r^2}{\frac{2}{3}\pi r^3}

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

\frac{S}{V}=\frac{3\pi r^2}{\frac{2}{3}\pi r^3} = \frac{9\pi r^2}{2\pi r^3}=\frac{9}{2r}

The answer is \frac{9}{2r}.

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:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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:

Explanation:

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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