Exercise 31 Page 914

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 Let's now consider the given diagram.

We know that r is equal to 1.5 centimeters. 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

Substitute

r= 1.5

A=1/2(4π ( 1.5^2))+π ( 1.5^2)

▼

Evaluate right-hand side

CalcPow

Calculate power

A=1/2(4π (2.25))+π (2.25)

CommutativePropMult

Commutative Property of Multiplication

A=1/2(4(2.25)π )+2.25π

Multiply

Multiply

A=1/2(9π )+2.25π

MoveRightFacToNumOne

1/b* a = a/b

A=9/2π+2.25π

CalcQuot

Calculate quotient

A=4.5π+2.25π

AddTerms

Add terms

A=6.75π

UseCalc

Use a calculator

A=21.205750...

RoundDec

Round to 1 decimal place(s)

A≈ 21.2

The area of the hemisphere to the nearest tenth is 21.2cm^2.