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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 6 Page 852

The volume of a hemisphere is half the volume of a sphere with the same radius.

1072.3cm^3

Practice makes perfect

A hemisphere is the name of a solid that is half of a sphere.

The volume of a hemisphere with radius r is half the volume of a sphere with radius r. Volume of a Hemisphere [0.8em] V=1/2(4/3π r^3) ⇔ V=2/3π r^3 To use this formula we first need to calculate the radius. To do so we will consider the given fact that the radius is half of the diameter. r=1/2d We can substitute 16 for d in the above formula and solve for the radius r.

r=1/2d

d= 16

r=1/2 16

MoveRightFacToNumOne

1/b* a = a/b

r=16/2

Calculate quotient

r=8

The radius measures 8cm. We can substitute this value in the formula for the volume of a hemisphere and simplify.

V=2/3π r^3

r= 8

V=2/3π ( 8)^3

Calculate power

V=2/3π(512)

CommutativePropMult

Commutative Property of Multiplication

V=2/3(512)π

MoveRightFacToNum

a/c* b = a* b/c

V=1024/3π

Use a calculator

V=1072.33...

Round to 1 decimal place(s)

V≈ 1072.3

The volume of the hemisphere to the nearest tenth is 1072.3cm^3.

Subchapter links

Exercises p.852-855