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Core Connections: Course 3 View details

Chapter Closure

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Exercise 73 Page 477

Use the formulas for the surface area and volume of a cylinder.

Surface Area: 402.1 square centimeters
Volume: 603.2 cubic centimeters

We are asked to find the surface area and the volume of the given cylinder. Let's start with the surface area.

Surface Area

Our cylinder has a diameter of 8 centimeters and a height of 12 centimeters.

If we divide the diameter by 2, we get the radius of the base. r=8/2=4cm Now we can use the following formula to calculate the surface area of the cylinder. S=2π rh+2π r^2 In this formula, r is the radius of the base and h is the height of the cylinder. Let's substitute 4 for r and 12 for h in the formula and solve for S.

S=2π rh+2π r^2

SubstituteII

r= 4, h= 12

S=2π( 4)( 12)+2π( 4)^2

▼

Evaluate right-hand side

CalcPow

Calculate power

S=2π( 4)(12)+2π(16)

Multiply

S=96π+32π

AddTerms

Add terms

S=128π

UseCalc

Use a calculator

S=402.123859...

RoundDec

Round to 1 decimal place(s)

S≈ 402.1

We found that the surface area of the cylinder is about 402.1 square centimeters.

Volume

The volume of a cylinder with the radius r and height h can be calculated by using the following formula. V=π r^2 h Since we are given both the radius and the height of the cylinder, we can substitute them into the formula and calculate V. Let's do it!

V=π r^2 h