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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 9 Page 875

Use the formula for the surface area of a sphere, and for the volume of a sphere.

Surface Area: About 514 718 540.4 km^2
Volume: About 1 098 066 219 443.5 km^3

The Earth can be modeled by the following sphere with a radius of r= 6400 km.

We are asked to find the volume and the surface area of the Earth and round the answer to the nearest tenth if necessary. Let's use the formula for the surface area of a sphere and for the volume of a sphere. First, let's find the surface area.

S=4π r^2

▼

Substitute 6400 for r and evaluate

r= 6400

S=4π ( 6400)^2

Calculate power

S=4π (40 960 000)

Multiply

S=163 840 000π

Use a calculator

S=514 718 540.364...

Round to 1 decimal place(s)

S≈ 514 718 540.4

Therefore, the surface area of the Earth is about 514 718 540.4 square kilometers. Now, let's find the volume of the Earth.

V=4/3π r^3

▼

Substitute 6400 for r and evaluate

r= 6400

V=4/3π( 6400)^3

Calculate power and product

V=4/3* 262 144 000 000π

MoveRightFacToNum

a/c* b = a* b/c

V=4* 262 144 000 000π/3

Multiply

V=1 048 576 000 000π/3

Use a calculator

V=1 098 066 219 443.523678...

Round to 1 decimal place(s)

V≈ 1 098 066 219 443.5

This tells us that the volume of the Earth is about 1 098 066 219 443.5 cubic kilometers.