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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 7 Page 852

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.

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 24πm. 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 /π.=.RHS /π.

24/π=2r

.LHS /2.=.RHS /2.

12=r

Rearrange equation

r=12

The radius measures 12m. 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

Calculate power

V=2/3π 1728

CommutativePropMult

Commutative Property of Multiplication

V=2/31728π

MoveRightFacToNum

a/c* b = a* b/c

V=3456/3π

Calculate quotient

V=1152π

Use a calculator

V=3619.11...

Round to 1 decimal place(s)

V≈ 3619.1

The volume of the hemisphere to the nearest tenth is 3619.1m^3.

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Exercises p.852-855