body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Surface Areas and Volumes of Spheres

Continue to next subchapter

Exercise 4 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.

161.4cm^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 circumference C of the great circle is approximately 26 cm. Let's recall the formula for circumference. C=2π r We can substitute 26 for C in this formula and solve for the radius r.

C=2π r

C= 26

26=2π r

▼

Solve for r

.LHS /2π.=.RHS /2π.

26/2π=r

CancelCommonFac

Cancel out common factors

13/π=r

Use a calculator

4.138 ≈ r

Rearrange equation

r ≈ 4.138

We know that r≈ 4.138cm. We can substitute this value into the formula for the area of a hemisphere and simplify.

A=1/2(4π r^2)+π r^2

r= 4.138

A=1/2(4π ( 4.138^2))+π ( 4.138^2)

▼

Evaluate right-hand side

Calculate power

A=1/2(4π (17.12))+π (17.12)

CommutativePropMult

Commutative Property of Multiplication

A=1/2(4(17.12)π )+17.12π

Multiply

A=1/2(68.48π )+17.12π

MoveRightFacToNumOne

1/b* a = a/b

A=68.48/2π+17.12π

Calculate quotient

A=34.24π+17.12π

Add terms

A=51.36π

Use a calculator

A=161.35...

Round to 1 decimal place(s)

A≈ 161.4

The area of the hemisphere to the nearest tenth is 161.4cm^2.

Subchapter links

Exercises p.852-855