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ISEE Upper Level Math : Spheres

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Example Question #8 : How To Find The Surface Area Of A Sphere

Find the surface area of a sphere with a radius of 6in.

Possible Answers:

$72\pi \text{ in}^2$

$144\pi \text{ in}^2$

$36\pi \text{ in}^2$

$121\pi \text{ in}^2$

$48\pi \text{ in}^2$

Correct answer:

$144\pi \text{ in}^2$

Explanation:

To find the surface area of a sphere, we will use the following formula:

$SA = 4\pi r^2$

where r is the radius of the sphere.

Now, we know the radius of the sphere is 6in. Knowing this, we can substitute into the formula. We get

$SA = 4 \cdot \pi \cdot (6\text{in})^2$

$SA = 4 \cdot \pi \cdot 36\text{in}^2$

$SA = 144\pi \text{ in}^2$

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Example Question #9 : How To Find The Surface Area Of A Sphere

Find the surface area of a sphere with a radius of 12in.

Possible Answers:

$216\pi \text{ in}^2$

$144\pi \text{ in}^2$

$432\pi \text{ in}^2$

$864\pi \text{ in}^2$

$576\pi \text{ in}^2$

Correct answer:

$576\pi \text{ in}^2$

Explanation:

To find the surface area of a sphere, we will use the following formula:

$SA = 4 \cdot \pi \cdot r^2$

where r is the radius of the sphere.

Now, we know the radius of the sphere is 12in.

Knowing this, we can substitute into the formula. We get

$SA = 4 \cdot \pi \cdot (12\text{in})^2$

$SA = 4 \cdot \pi \cdot 144\text{in}^2$

$SA = 576\pi \text{ in}^2$

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Example Question #10 : How To Find The Surface Area Of A Sphere

Find the surface area of a sphere with a diameter of 20in.

Possible Answers:

$600\pi \text{ in}^2$

$800\pi \text{ in}^2$

$200\pi \text{ in}^2$

$300\pi \text{ in}^2$

$400\pi \text{ in}^2$

Correct answer:

$400\pi \text{ in}^2$

Explanation:

To find the surface area of a sphere, we will use the following formula:

$SA = 4 \cdot \pi \cdot r^2$

where r is the radius of the sphere.

Now, we know the diameter of the sphere is 20in. We also know the diameter is two times the radius. Therefore, the radius is 10in.

Knowing this, we can substitute into the formula. We get

$SA = 4 \cdot \pi \cdot (10\text{in})^2$

$SA = 4 \cdot \pi \cdot 100\text{in}^2$

$SA = 400 \pi \text{ in}^2$

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Example Question #411 : Geometry

Find the surface area of a sphere with a diameter of 12in.

Possible Answers:

$96\pi \text{ in}^2$

$108\pi \text{ in}^2$

$48\pi \text{ in}^2$

$144\pi \text{ in}^2$

$121\pi \text{ in}^2$

Correct answer:

$144\pi \text{ in}^2$

Explanation:

To find the surface area of a sphere, we will use the following formula:

$SA = 4\pi r^2$

where r is the radius of the sphere.

Now, we know the diameter of the sphere is 12in. We also know the diameter is two times the radius. Therefore, the radius is 6in. So, we get

$SA = 4 \cdot \pi \cdot (6\text{in})^2$

$SA = 4 \cdot \pi \cdot 36\text{in}^2$

$SA = 144\pi \text{ in}^2$

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Example Question #21 : Spheres

A spherical buoy has a radius of meters. What is the surface area of the buoy?

Possible Answers:

$100\pi m^2$

100 m^2

50 m^2

75m^2

$50\pi m^2$

Correct answer:

$100\pi m^2$

Explanation:

A spherical buoy has a radius of 5 meters. What is the surface area of the buoy?

To find the surface area of a sphere, use the following:

$SA_{sphere}=4\pi r^2$

Plug in our radius and solve!

$SA_{sphere}=4\pi (5m)^2=100\pi m^2$

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ISEE Upper Level Math : Spheres

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #8 : How To Find The Surface Area Of A Sphere

Example Question #9 : How To Find The Surface Area Of A Sphere

Example Question #10 : How To Find The Surface Area Of A Sphere

Example Question #411 : Geometry

Example Question #21 : Spheres

All ISEE Upper Level Math Resources

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