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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 4 Page 435

Use the formula for the volume of a cone.

≈ 4 m

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 46 cubic meters and the height of the base is 2.75 meters. Let's substitute these values into the formula and solve it for r.

V=1/3π r^2 h

V= 46, h= 2.75

46=1/3π r^2 ( 2.75)

▼

Simplify right-hand side

CommutativePropMult

Commutative Property of Multiplication

46=1/3(2.75π r^2)

MoveRightFacToNumOne

1/b* a = a/b

46=2.75π r^2/3

LHS * 3=RHS* 3

3* 46=3 * 2.75π r^2/3

DenomMultFracToNumber

3 * a/3= a

3* 46 = 2.75 π r^2

Multiply

138=2.75 π r^2

.LHS /2.75π.=.RHS /2.75π.

138/2.75π=2.75π r^2/2.75π

Cross out common factors

138/2.75π=2.75πr^2/2.75π

Calculate quotient

138/2.75π=r^2

sqrt(LHS)=sqrt(RHS)

sqrt(138/2.75π)= sqrt(r^2)

sqrt(a^2)=± a

± sqrt(138/2.75π)= r

Rearrange equation

r=± sqrt(138/2.75π)

Use a calculator

r=± 3.996669...

Round to nearest integer

r≈ ± 4

Because radius are always nonnegative, we can conclude that the radius of the cone is about 4 meters.

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