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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

5. Volumes of Pyramids and Cones

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Exercise 18 Page 730

Use the formula for the volume of a cone.

Exact Solution: 22/3πin.^3
Approximate Solution: 23in.^3

Practice makes perfect

The given solid is a cone.

To calculate the volume of a cone, we can use the following formula. V= 13π r^2 h Here r is the radius and h is the height of the cone. We are given that the height of the cone is 5 12in. and the diameter of the base is 4in. The diameter is twice as long as radius, so radius of the base is 2in. Let's substitute these values into the above formula and calculate the volume.

V=1/3π r^2 h

r= 2, h= 5 12

V=1/3π ( 2)^2 ( 51/2)

▼

Simplify right-hand side

Calculate power

V=1/3π(4)(51/2)

a bc=a* c+b/c

V=1/3π(4)(11/2)

MoveLeftFacToNum

a*b/c= a* b/c

V=1/3π(4* 11/2)

a/b=.a /2./.b /2.

V=1/3π(2* 11)

CommutativePropMult

Commutative Property of Multiplication

V=1/3(2* 11)π

MoveRightFacToNumOne

1/b* a = a/b

V=2*11/3π

Multiply

V=22/3π

The volume of the cone is 223π cubic inches. We were asked to round it to the nearest cubic inch, so let's do it!

V=22/3π

Use a calculator

V=23.038346...

Round to nearest integer

V=23

The rounded volume of the cone is 23 cubic inches.

Subchapter links

Lesson Check p.729

Practice and Problem-Solving Exercises p.729-732

Standardized Test Prep p.732

Mixed Review p.732