Exercise 10 Page 624

We are given a candle that is 6inches tall and 2.5inches across. Using the fact that the candle is a cylinder, we can draw it.

We are asked to find the least amount of paper that will be needed to wrap the candle with no overlap. To do so, we need to calculate the surface area of the candle. Let's start by recalling that the surface area of a cylinder is the lateral area plus the area of the two circular bases. To calculate the surface area of a cylinder, we can use the following formula. S=2π rh+2π r^2 In this formula, r is the radius of the base and h is the height of the cylinder. Note that we know the height and the diameter of the cylindrical candle. To find the radius of the candle, we can divide the diameter by 2.

r = d/2

Substitute

d= 2.5

r = 2.5/2

CalcQuot

Calculate quotient

r = 1.25

Therefore, the radius is equal to 1.25 inches. Now, we can substitute the height and the radius into the formula and calculate the surface area of the candle. Let's do it!

S=2π rh+2π r^2

SubstituteII

r= 1.25, h= 6

S=2π( 1.25)( 6)+2π( 1.25)^2

▼

Simplify right-hand side

CalcPow

Calculate power

S=2π(1.25)(6)+2π(1.5625)

Multiply

Multiply

S=15π+3.125π

AddTerms

Add terms

S=18.125π

UseCalc

Use a calculator

S=56.941...

RoundDec

Round to 1 decimal place(s)

S≈ 56.9

We got that the total surface area of the candle is about 56.9 square inches. This means that the least amount of paper needed to wrap the candle with no overlap is also about 56.9 square inches.