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McGraw Hill Glencoe Geometry, 2012

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McGraw Hill Glencoe Geometry, 2012 View details

Study Guide and Review

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Exercise 26 Page 905

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

≈ 461.8 in.^2

Practice makes perfect

A hemisphere is half of a sphere.

Therefore, 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 a 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 radius is half of the diameter. r=1/2d We can substitute 14 for d in this formula and solve for the radius r.

r=1/2d

d= 14

r=1/2( 14)

▼

Simplify right-hand side

MoveRightFacToNumOne

1/b* a = a/b

r=14/2

Calculate quotient

r=7

We know that r=7 inches. We can substitute this value in the formula for the area of a hemisphere and simplify.

A=1/2(4π r^2)+π r^2

r= 7

A=1/2(4π ( 7^2))+π ( 7^2)

▼

Evaluate right-hand side

Calculate power

A=1/2(4π(49) )+π(49)

CommutativePropMult

Commutative Property of Multiplication

A=1/2(4* 49π )+49π

Multiply

A=1/2(196π)+49π

MoveRightFacToNumOne

1/b* a = a/b

A=196/2π+49π

Calculate quotient

A=98π+49π

Add terms

A=147π

Use a calculator

A=461.81412...

Round to 1 decimal place(s)

A≈ 461.8

The area of the hemisphere is about 461.8 square inches.