Question

section 11.7 homework
page 3

1. find the surface area of a sphere whose volume is \\(288\pi\text{ cm}^3\\).

1. if the radius of the base of a hemisphere (which is bounded by a great circle) is \\(r\\), what is the area of the great circle? what is the total surface area of the hemisphere, including the base? how do they compare?

Explanation:

Find the radius of the sphere

Using the Sphere Volume knowledge point

$$
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$$

Calculate the surface area of the sphere

Using the Sphere Surface Area knowledge point

$$
LATEXBLOCK1
$$

Find the area of the great circle

Using the Great Circle Area knowledge point

$$
LATEXBLOCK2
$$

Calculate the total surface area of the hemisphere

Using the Hemisphere Properties and Sphere Surface Area knowledge points

$$
LATEXBLOCK3
$$

Compare the two areas

Using the Great Circle Area and Hemisphere Properties knowledge points

$$
LATEXBLOCK4
$$

Answer:

Question 6

The surface area of the sphere is \(144\pi\text{ cm}^2\).

Question 7

• The area of the great circle is \(\pi r^2\).
• The total surface area of the hemisphere, including the base, is \(3\pi r^2\).
• The total surface area of the hemisphere is exactly 3 times the area of its great circle base.