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Glencoe Math: Course 3, Volume 2

GM

Glencoe Math: Course 3, Volume 2 View details

5. Surface Area of Cones

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Exercise 38 Page 638

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

1286.2ft^3

Practice makes perfect

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

Therefore, 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 hemisphere.

In the diagram we can see that the diameter is 17 feet. Therefore, the radius is 17÷ 2= 8.5 feet. We can substitute this value for r in the formula for the volume of a hemisphere and simplify.

V=2/3π r^3

r= 8.5

V=2/3π ( 8.5)^3

▼

Evaluate right-hand side

Calculate power

V=2/3π(614.125)

CommutativePropMult

Commutative Property of Multiplication

V=2/3(614.125)π

MoveRightFacToNum

a/c* b = a* b/c

V=2(614.125)/3π

Multiply

V=1228.25/3π

Calculate quotient

V=409.416π

Use a calculator

V=1286.220392...

Round to 1 decimal place(s)

V≈ 1286.2

The volume of the hemisphere, to the nearest tenth, is 1286.2 cubic feet.

Subchapter links

Guided Practice p.634

Independent Practice p.635-636

H.O.T. Problems p.636

Extra Practice p.637

Standardized Test Practice p.638

Common Core Review p.638