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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Surface Areas and Volumes of Spheres

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Exercise 12 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.

109.0mm^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 the great circle. Surface Area of a Hemisphere [0.8em] A=1/2(4π r^2)+π r^2 We know that r=3.4mm. 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= 3.4

A=1/2(4π ( 3.4^2))+π ( 3.4^2)

▼

Evaluate right-hand side

Calculate power

A=1/2(4π (11.56))+π (11.56)

CommutativePropMult

Commutative Property of Multiplication

A=1/2(4(11.56)π )+11.56π

Multiply

A=1/2(46.24π )+11.56π

MoveRightFacToNumOne

1/b* a = a/b

A=46.24/2π+11.56π

Calculate quotient

A=23.12π+11.56π

Add terms

A=34.68π

Use a calculator

A=108.95...

Round to 1 decimal place(s)

A≈ 109.0

The area of the hemisphere to the nearest tenth is 109.0mm^2.

Subchapter links

Exercises p.852-855