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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

6. Surface Areas and Volumes of Spheres

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Exercise 60 Page 740

Use the formula for the surface area.

B

Practice makes perfect

We are told that the surface area of a sphere is 100π m^2 and want to find its diameter.

We first need to find its radius. We know that the surface area of a sphere is four times the product of π and the square of the radius. S.A.=4π r^2 Let's substitute 100π for S.A. in the formula and solve for r.

S.A.=4π r^2

S.A.= 100π

100π=4π r^2

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Solve for r

.LHS /4π.=.RHS /4π.

100/4=r^2

Calculate quotient

25=r^2

Rearrange equation

r^2=25

sqrt(LHS)=sqrt(RHS)

r=sqrt(25)

Calculate root

r=5

Note that, when solving the above equation, we kept the principal root. This is because r is the radius of a sphere and therefore must be positive. The radius of a sphere with surface area 100π m^2 is 5m. This means its diameter is 2(5)=10m. This corresponds to option B.

Subchapter links

Lesson Check p.736

Practice and Problem-Solving Exercises p.737-739

Standardized Test Prep p.740

Mixed Review p.740