McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
Mid-Chapter Quiz
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Exercise 8 Page 840

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

Lateral Area: 2591.8 yd^2
Surface Area: 3779.7 yd^2

Let's calculate the lateral area and then surface area of the given cylinder.

Lateral Area

To calculate the lateral area of a cylinder, we can use the following formula. L=2π rhIn this formula, r is the radius of the base and h is the height of the cylinder. We know that the diameter d of a circle is equal to 27.5yd and is exactly twice as long as its radius. d=2r ⇒ r= d2= 27.52=13.75yd Substituting r with 13.75 and h with 30 into the formula, and simplify.
L=2π rh
L=2π( 13.75)( 30)
Simplify right-hand side
L=825π
L=2591.813939...
L≈ 2591.8
We know that lateral area is 825π or about 2591.8 yd^2.

Surface Area

To calculate the surface area of a cylinder, we can use the following formula. S=L+2π r^2 In this formula, L is the lateral area of the cylinder and r is the radius of the base. Substituting L with 825π and r with 13.75 into the formula, and find S. Let's do it!
S=L+2π r^2
S= 825π+2π(13.75)^2
Simplify right-hand side
S=825π+2π(189.0625)
S=825π+378.125π
S=1203.125π
S=3779.728661...
S≈ 3779.7
The surface area of the cylinder is about 3779.7 yd^2.