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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 5 Page 435

Use the formula for the volume of a cone.

≈ 314.2 yd^3

Practice makes perfect

We want to find the volume of a cone with a diameter of 10 yards and a height of 12 yards. Let's start by drawing the cone!

Now 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 height of the cone is 12 yards and the diameter of the base is 10 yards. Note that if we divide the diameter by 2, we get the radius of the base. r=10/2=5yd Let's substitute r= 5 and h= 12 into the formula and calculate the volume.

V=1/3π r^2 h

r= 5, h= 12

V=1/3π ( 5)^2 ( 12)

▼

Simplify right-hand side

Calculate power

V=1/3π(25)(12)

Multiply

V=1/3π(300)

CommutativePropMult

Commutative Property of Multiplication

V=1/3(300π)

MoveRightFacToNumOne

1/b* a = a/b

V=300π/3

Calculate quotient

V=100π

Use a calculator

V=314.159265...

Round to 1 decimal place(s)

V≈ 314.2

The volume of the cone is 314.2 cubic 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