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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

If the radius of the sphere is one half, what is the surface area?

Possible Answers:

$\pi$

$\frac{4}{3}\pi$

$\frac{1}{4}\pi$

$2\pi$

$\frac{1}{2}\pi$

Correct answer:

$\pi$

Explanation:

Write the formula for the surface area of a sphere, plug in the radius, and find the area.

$A=4\pi r^2 = 4\pi \left(\frac{1}{2}\right)^2 = 4\pi\left(\frac{1}{4}\right)= \pi$

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

If the diameter of a sphere is , what is the surface area?

Possible Answers:

$500\pi$

$225\pi$

$900\pi$

$42\pi$

$56.25\pi$

Correct answer:

$225\pi$

Explanation:

The radius is half the length of a diameter.

$r=\frac{d}{2}=\frac{15}{2}=7.5$

Write the formula for the surface area of a sphere and plug in the radius.

$A=4\pi r^2 = 4\pi(7.5)^2= 225\pi$

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Example Question #44 : Spheres

Find the surface area of a sphere if the volume is .

Possible Answers:

$\sqrt[3]{9}$

$\left(\frac{3}{4\pi}\right)^\frac{2}{3}$

$\sqrt[3]{\frac{3\pi}{4}}$

$4\pi\left(\frac{4}{3\pi}\right)^\frac{2}{3}$

$4\pi\left(\frac{3}{4\pi}\right)^\frac{2}{3}$

Correct answer:

$4\pi\left(\frac{3}{4\pi}\right)^\frac{2}{3}$

Explanation:

Write the formula for the volume of a sphere and substitute volume to find radius.

$V=\frac{4}{3}\pi r^3$

$1=\frac{4}{3}\pi r^3$

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

$r=\sqrt[3]{\frac{3}{4\pi}}= (\frac{3}{4\pi})^\frac{1}{3}$

Write the formula for the surface area of a sphere and plug in the radius.

$A=4\pi r^2 = 4\pi \left[\left(\frac{3}{4\pi}\right)^\frac{1}{3}\right]^2 = 4\pi\left(\frac{3}{4\pi}\right)^\frac{2}{3}$

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

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

Possible Answers:

37.70

32.60

39.60

38.80

Correct answer:

37.70

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.

$\text{Surface Area of Hemisphere}=3\pi (2)^2=37.70$

Make sure to round to places after the decimal.

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

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

Possible Answers:

84.82

85.22

79.40

86.08

Correct answer:

84.82

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.

$\text{Surface Area of Hemisphere}=3\pi (3)^2=84.82$

Make sure to round to places after the decimal.

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Example Question #1241 : Intermediate Geometry

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

Possible Answers:

147.87

150.80

156.60

144.23

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 #11 : 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:

1.73

2.36

1.95

3.26

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 #1243 : Intermediate Geometry

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

Possible Answers:

235.62

226.87

248.09

252.15

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:

347.11

326.09

356.59

339.29

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

461.81

412.08

445.01

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

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All Intermediate Geometry Resources

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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

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

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

Example Question #44 : Spheres

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 #1241 : Intermediate Geometry

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

Example Question #1243 : Intermediate Geometry

Example Question #51 : Spheres

Example Question #52 : Spheres

All Intermediate Geometry Resources

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