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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 28 Page 873

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

3619.1m^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 fact that the circumference of a great circle is 24π meters. Let's recall the formula for the circumference of a circle with radius r. C=2π r We can substitute 24π for C in the above formula and solve for the radius r.

C=2π r

C= 24π

24π=2π r

▼

Solve for r

.LHS /2π.=.RHS /2π.

12=r

Rearrange equation

r=12

The radius measures 12 meters. We can substitute this value in the formula for the volume of a hemisphere and simplify.

V=2/3π r^3

r= 12

V=2/3π ( 12)^3

▼

Evaluate right-hand side

Calculate power

V=2/3π(1728)

CommutativePropMult

Commutative Property of Multiplication

V=2/3(1728π)

MoveRightFacToNum

a/c* b = a* b/c

V=3456π/3

Calculate quotient

V=1152π

Use a calculator

V=3619.11473...

Round to 1 decimal place(s)

V≈ 3619.1

The volume of the hemisphere is about 3619.1 cubic meters.

Subchapter links

1 Representations of Three-Dimensional Figures p.872

2 Surface Areas of Prisms and Cylinders p.872

3 Surface Areas of Pyramids and Cones p.872

4 Volumes of Prisms and Cylinders p.873

5 Volumes of Pyramids and Cones p.873

6 Surface Areas and Volumes of Spheres p.873

7 Spherical Geometry p.874

8 Congruent and Similar Solids p.874