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Glencoe Math: Course 3, Volume 2

GM

Glencoe Math: Course 3, Volume 2 View details

2. Volume of Cones

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Exercise 23 Page 603

Use the formula for the volume of a cone.

Approximately 15in.

Practice makes perfect

Consider the given cone. Its height is 8 inches and the volume is 471.24 cubic inches.

To find the diameter we want to find the radius first. We can use the formula for the volume of a cone. V= 13π r^2 h Here, r is the radius and h is the height of the cone. We are given that the height of the cone is 8 inches. The volume is 471.24 cubic inches. Let's substitute these values into the formula and solve for the radius r.

V=1/3π r^2 h

V= 471.24, h= 8

471.24=1/3π r^2 ( 8)

▼

Solve for r

CommutativePropMult

Commutative Property of Multiplication

471.24 = 1/3 (8)π r^2

LHS * 3=RHS* 3

1413.72 = 8π r^2

.LHS /8.=.RHS /8.

176.715 = π r^2

.LHS /π.=.RHS /π.

176.715/π = r^2

Rearrange equation

r^2 = 176.715/π

Use a calculator

r^2 = 56.250132...

sqrt(LHS)=sqrt(RHS)

r = sqrt(56.250132...)

Use a calculator

r = 7.500009...

Round to 1 decimal place(s)

r ≈ 7.5

We found out that the approximate length of the radius is r=7.5. We can finally find the diameter.

d = 2r

r= 7.5

d = 2( 7.5)

Multiply

d = 15

Since the length of the radius was approximated, the diameter of 15 inches is also an approximation.

Subchapter links

Guided Practice p.600

Independent Practice p.601-602

H.O.T. Problems p.602

Standardized Test Practice p.602-604

Extra Practice p.603

Common Core Review p.604