Exercise 5 Page 450

We want to find the surface area and the lateral surface area of the given cylinder. The cylinder has a diameter of 22 inches and the height of 12.5 inches.

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 diameter is 22 inches, so the radius is 22÷2 = 11 inches. By substituting 11 for r and 12.5 for h in the above formula, we can solve for S. Let's do it!

L=2π rh

SubstituteII

r= 11, h= 12.5

L=2π( 11)( 12.5)

Multiply

Multiply

L=275π

UseCalc

Use a calculator

L=863.937979...

RoundDec

Round to 1 decimal place(s)

L ≈ 863.9

We found that the lateral surface area of the cylinder is about 863.9 square inches. 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 ≈ 863.9 square inches and r = 11 inches. Let's substitute these values into our formula and find the surface area!

S = L + 2 π r^2

r ≈ 11, L ≈ 863.9

S ≈ 863.9 + 2 π ( 11)^2

▼

Simplify right-hand side

CalcPow

Calculate power

S ≈ 863.9 + 2 π (121)

Multiply

Multiply

S ≈ 863.9 + 242 π

UseCalc

Use a calculator

S ≈ 1624.165422...

RoundDec

Round to 1 decimal place(s)

S ≈ 1624.2

The surface area of our cylinder is about 1624.2 square inches.