Exercise 4 Page 450

We want to find the surface area and the lateral surface area of the given cylinder.

The surface area of a cylinder is a sum of its lateral surface area and the areas of the two bases.

Lateral Surface Area

To calculate the lateral surface area of a cylinder, we can use the following formula. L=2π rh In this formula, r is the radius of the base and h is the height of the cylinder. In our case, the base's radius is 2 centimeters and the height is 3 centimeters. By substituting 2 for r with 3 for h in the above formula, we can solve for S. Let's do it!

L=2π rh

SubstituteII

r= 2, h= 3

L=2π( 2)( 3)

Multiply

Multiply

L=12π

UseCalc

Use a calculator

L=37.699111...

RoundDec

Round to 1 decimal place(s)

L ≈ 37.7

We found that the lateral surface area of the cylinder is about 37.7 square centimeters. Now, let's find the surface area of the cylinder.

Surface Area

The surface area of a cylinder is a sum of the lateral surface area and the areas of the two circular bases. We can find it using the following formula. S = L + 2 π r^2 Here, L is the lateral surface area and r is the radius of the base. In our case, L ≈ 37.7 square centimeters and r = 2 centimeters. Let's substitute these values into our formula and find the surface area!

S = L + 2 π r^2

SubstituteII

r= 2, L= 37.7

S = 37.7 + 2 π ( 2)^2

▼

Simplify right-hand side

CalcPow

Calculate power

S = 37.7 + 2 π (4)

Multiply

Multiply

S = 37.7+ 8 π

UseCalc

Use a calculator

S = 62.832741...

RoundDec

Round to 2 decimal place(s)

S ≈ 62.83

The surface area of our cylinder is about 62.83 square centimeters.