Exercise 4 Page 653

We are given that a cone-shaped icicle has a diameter of 2 centimeters and a slant height of 8 centimeters. Let's draw this icicle!

We are asked to find the lateral area and the total surface area of the icicle. We will start with the lateral area. Let's start by recalling that the lateral area of a cone is one-half the circumference of the base times the slant height. To calculate the lateral area of a cone, we can use the following formula. L.A.=π rlIn this formula, r is the radius of the base and l is the slant height of the cone. Note that we know the diameter and the slant height of the cone-shaped icicle. To find the radius of the icicle, we can divide the diameter by 2.

r = d/2

Substitute

d= 2

r = 2/2

CalcQuot

Calculate quotient

r = 1

Therefore, the radius is equal to 1 centimeter. Now we can substitute the slant height and the radius into the formula and calculate the lateral area.

L.A.=π rl

SubstituteII

r= 1, l= 8

L.A.=π ( 1)( 8)

▼

Simplify right-hand side

IdPropMult

Identity Property of Multiplication

L.A.=8π

UseCalc

Use a calculator

L.A.=25.132741...

RoundDec

Round to 1 decimal place(s)

L.A.≈ 25.1

We got that the lateral area of the icicle is about 25.1 square centimeters. Next, let's use the following formula to find the total surface area. S.A.=π rl+π r^2 We can substitute the slant height and the radius into the formula and calculate the total surface area of the icicle.

S.A.=π rl+π r^2

SubstituteII

r= 1, h= 8

S.A.=π( 1)( 8)+π( 1)^2

▼

Simplify right-hand side

BaseOne

1^a=1

S.A.=π( 1)(8)+π(1)

IdPropMult

Identity Property of Multiplication

S.A.=8π+π

AddTerms

Add terms

S.A.=9π

UseCalc

Use a calculator

S.A.=28.274333...

RoundDec

Round to 1 decimal place(s)

S.A.≈ 28.3

Therefore, the total surface area of the icicle is about 28.3 square centimeters.