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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Volumes of Pyramids and Cones

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Exercise 19 Page 845

Use the formula for the volume of a cone.

1473.1cm^3

Practice makes perfect

To calculate the volume of a cone, we can use the following formula. In this formula r is the radius, and h is the height of a cone. V= 13π r^2 h We are given that the radius of the cone is 8 cm. Let's look at the triangle including the height and the radius of the cone.

The trigonometric function which connect these two lengths and the angle is tangent. tan(θ )=opposite/adjacent Let's substitute the values and calculate the radius.

tan(θ )=opposite/adjacent

SubstituteValues

Substitute values

tan(20^(∘))=8/h

▼

Solve for h

LHS * h=RHS* h

htan20^(∘)=8

.LHS /tan20^(∘).=.RHS /tan20^(∘).

h=8/tan20^(∘)

Use a calculator

h=21.97981...

Round to 2 decimal place(s)

h=21.98

We found that the height of the cone is approximately 21.98. Now we have all values to calculate the volume.

V=1/3π r^2 h

r= 8, h= 21.98

V=1/3π ( 8)^2 ( 21.98)

▼

Simplify right-hand side

Calculate power

V=1/3π(64)(21.98)

Multiply

V=1406.72/3π

Use a calculator

V=1473.11...

Round to 1 decimal place(s)

V≈ 1473.1

The volume of the cone is approximately 1473.1cm^3.

Subchapter links

Exercises p.844-847