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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 2 Page 434

Use the formula for the volume of a cone.

≈ 30.6yd

Practice makes perfect

We want to find the height 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 7200 cubic yards and the radius of the base is 15 yards. Let's substitute these values into the formula and solve it for h.

V=1/3π r^2 h

V= 7200, r= 15

7200=1/3π ( 15)^2 h

▼

Solve for h

Calculate power

7200=1/3π(225)h

CommutativePropMult

Commutative Property of Multiplication

7200=1/3(225π h)

MoveRightFacToNumOne

1/b* a = a/b

7200=225π h/3

Calculate quotient

7200=75π h

.LHS /75π.=.RHS /75π.

7200/75π=75π h/75π

Cross out common factors

7200/75π=75πh/75π

Calculate quotient

7200/75π=h

Rearrange equation

h=7200/75π

Use a calculator

h=30.557749...

Round to 1 decimal place(s)

h≈ 30.6

The height of the cone is 30.6 yards.

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