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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

1. Volumes of Cylinders

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Exercise 4 Page 429

Use the formula for the volume of a cylinder.

6.5 millimeters

Practice makes perfect

We are given the following cylinder and we want to find the value of its height.

The volume of a cylinder with the radius r and height h can be calculated by the following formula. V=π r^2 h Since we are given the volume and height of the cylinder, we can substitute them into the formula and calculate its radius.

V=π r^2 h

V= 564, h= 4.25

564=π r^2 ( 4.25)

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Solve for r

CommutativePropMult

Commutative Property of Multiplication

564=4.25π r^2

π= 3.141592...

564=4.25( 3.141592...) r^2

Multiply

564=13.351768... r^2

.LHS /13.351768....=.RHS /13.351768....

564/13.351768...=13.351768... r^2/13.351768...

CancelCommonFac

Cancel out common factors

564/13.351768...=13.351768... r^2/13.351768...

Simplify quotient

564/13.351768...=r^2

Calculate quotient

42.241496...=r^2

Rearrange equation

r^2=42.241496...

sqrt(LHS)=sqrt(RHS)

r=sqrt(42.241496...)

Calculate root

r=6.499353...

Round to 1 decimal place(s)

r ≈ 6.5

Therefore, the height of the cylinder is about 6.5 millimeters.

Subchapter links

Try It p.428-429

Self-Assessment for Concepts & Skills p.429

Self-Assessment for Problem Solving p.430

Review & Refresh p.431

Concepts, Skills, & Problem Solving p.431-432