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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

2. Volumes of Cones

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Exercise 3 Page 435

Use the formula for the volume of a cone.

≈ 5 ft

Practice makes perfect

We want to find the radius of the given cone.

To do so, we can use the formula for the volume of a cone. V=1/3 B h Here, B is the area of the base and h is the height of the cone. Since the base is a circle, the area of the base will be equal to π r^2, where r is the radius. V= 1/3 π r^2 h We are given that the volume of the cone is 183 cubic feet and the height of the base is 7 feet. Let's substitute these values into the formula and solve it for r.

V=1/3π r^2 h

V= 183, h= 7

183=1/3π r^2 ( 7)

▼

Solve for r

CommutativePropMult

Commutative Property of Multiplication

183=1/3(7π r^2)

MoveRightFacToNumOne

1/b* a = a/b

183=7π r^2/3

LHS * 3=RHS* 3

3* 183=3 * 7π r^2/3

DenomMultFracToNumber

3 * a/3= a

3* 183 = 7 π r^2

Multiply

549=7 π r^2

.LHS /7π.=.RHS /7π.

549/7π=7π r^2/7π

Cross out common factors

549/7π=7πr^2/7π

Calculate quotient

549/7π=r^2

sqrt(LHS)=sqrt(RHS)

sqrt(549/7π)= sqrt(r^2)

sqrt(a^2)=± a

± sqrt(549/7π)= r

Rearrange equation

r=± sqrt(549/7π)

Use a calculator

r=± 4.996457...

Round to 1 decimal place(s)

r≈ ± 5

Because radius are always nonnegative, we can conclude that the radius of the cone is about 5 feet.

Subchapter links

Try It p.434-435

Self-Assessment for Concepts & Skills p.435

Self-Assessment for Problem Solving p.436

Review & Refresh p.437

Concepts, Skills, & Problem Solving p.437-438