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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Preparing for Standardized Tests

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Exercise 1 Page 877

The lateral area of a right cone is L=π r l, where r is the radius and l is the slant height of the cone.

About 10 millimeters

Practice makes perfect

Let r denote the radius of the given right circular cone. Since the slant height l is twice the radius, we get that l=2 r.

The lateral area L of the cone is about 569 square millimeters. Furthermore, it is given by the formula L=π r l. We are asked to find the radius and round our answer to the nearest whole millimeter. Let's use the formula for L and substitute the known expressions.

L=π r l

L= 569, l= 2 r

569=π r * 2 r

▼

Solve for r

Multiply

569=2π r^2

.LHS /2π.=.RHS /2π.

569/2π= r^2

Rearrange equation

r^2=569/2π

Use a calculator

r^2=90.559162...

sqrt(LHS)=sqrt(RHS)

sqrt(r^2)=sqrt(90.559162...)

SqrtPowToNumber

sqrt(a^2)=a

r=sqrt(90.559162...)

Use a calculator

r=9.516257...

Round to nearest integer

r≈ 10

The radius is about 10 millimeters.

Subchapter links

Exercises p.877