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McGraw Hill Integrated II, 2012 View details

6. Surface Areas and Volumes of Spheres

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Exercise 16 Page 852

To find the area of a hemisphere, calculate the area of half of a sphere with the same radius and add the area of the great circle.

122.2in^2

Practice makes perfect

A hemisphere is half of a sphere.

To find the area of a hemisphere we need to calculate the area of half of a sphere with the same radius and add the area of the great circle. Surface Area of a Hemisphere [0.8em] A=1/2(4π r^2)+π r^2 We first need to calculate the radius. To do so, we will consider the given fact that the area of a circle A of the great circle is 40 in^2. Let's recall the formula for the area. A=π r^2 We can substitute 40 for A in this formula and solve for the radius r.

A=π r^2

Substitute

A= 40

40=π r^2

▼

Solve for r

DivEqn

.LHS /π.=.RHS /π.

40/π=r^2

RearrangeEqn

Rearrange equation

r^2=40/π