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Intermediate Geometry : How to find the surface area of a sphere

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Example Question #11 : How To Find The Surface Area Of A Sphere

Find the surface area of a hemisphere that has a radius of .

Possible Answers:

147.87

150.80

144.23

156.60

Correct answer:

150.80

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (4)^2=150.80$

Make sure to round to places after the decimal.

Report an Error

Example Question #12 : How To Find The Surface Area Of A Sphere

Find the surface area for a hemisphere that has a radius of $\frac{1}{2}$ .

Possible Answers:

3.26

1.95

2.36

1.73

Correct answer:

2.36

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (\frac{1}{2})^2=2.36$

Make sure to round to places after the decimal.

Report an Error

Example Question #13 : How To Find The Surface Area Of A Sphere

Find the surface area of a hemisphere that has a radius of .

Possible Answers:

235.62

252.15

248.09

226.87

Correct answer:

235.62

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (5)^2=235.62$

Make sure to round to places after the decimal.

Report an Error

Example Question #51 : Spheres

Find the surface area of a hemisphere that has a radius of .

Possible Answers:

356.59

339.29

326.09

347.11

Correct answer:

339.29

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (6)^2=339.29$

Make sure to round to places after the decimal.

Report an Error

Example Question #52 : Spheres

Find the surface area of a hemisphere if it has a radius of .

Possible Answers:

495.87

445.01

412.08

461.81

Correct answer:

461.81

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (7)^2=461.81$

Make sure to round to places after the decimal.

Report an Error

Example Question #53 : Spheres

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

Possible Answers:

625.88

603.19

608.08

623.35

Correct answer:

603.19

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (8)^2=603.19$

Make sure to round to places after the decimal.

Report an Error

Example Question #54 : Spheres

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

Possible Answers:

905.67

942.48

933.62

958.87

Correct answer:

942.48

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (10)^2=942.48$

Make sure to round to places after the decimal.

Report an Error

Example Question #55 : Spheres

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

Possible Answers:

1258.25

1000.27

1323.98

1140.40

Correct answer:

1140.40

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (11)^2=1140.40$

Make sure to round to places after the decimal.

Report an Error

Example Question #56 : Spheres

Find the surface area of a hemisphere that has a radius of $\frac{1}{4}$ .

Possible Answers:

0.59

0.58

0.67

0.81

Correct answer:

0.59

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (\frac{1}{4})^2=0.59$

Make sure to round to places after the decimal.

Report an Error

Example Question #57 : Spheres

Find the surface area of a hemisphere that has a radius of $\frac{3}{2}$ .

Possible Answers:

20.59

23.23

24.84

21.21

Correct answer:

21.21

Explanation:

In order to find the area of a hemisphere, which is just half a sphere, you will need to first find half the surface area of the sphere.

Recall how to find the surface area of a sphere:

$\text{Surface Area of Sphere}=4\pi r^2$ , where is the radius.

Now, since the sphere is cut in half, it also has a circle as its base.

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi r^2$

Now add together half the surface area of a sphere with the area of the circular base to find the surface area of a hemisphere.

$\text{Surface Area of Hemisphere}=2\pi r^2+\pi r^2=3 \pi r^2$

Plug in the given radius to find the surface area.

$\text{Surface Area of Hemisphere}=3\pi (\frac{3}{2})^2=21.21$

Make sure to round to places after the decimal.

Report an Error

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Intermediate Geometry : How to find the surface area of a sphere

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #11 : How To Find The Surface Area Of A Sphere

Example Question #12 : How To Find The Surface Area Of A Sphere

Example Question #13 : How To Find The Surface Area Of A Sphere

Example Question #51 : Spheres

Example Question #52 : Spheres

Example Question #53 : Spheres

Example Question #54 : Spheres

Example Question #55 : Spheres

Example Question #56 : Spheres

Example Question #57 : Spheres

All Intermediate Geometry Resources

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