McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
Mid-Chapter Quiz
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Exercise 9 Page 840

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

Lateral Area: 263.9 m^2
Surface Area: 320.4 m^2

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

Lateral Area

To calculate the lateral 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. Substitute r with 3 and h with 14 into the formula and simplify.
L=2π rh
L=2π( 3)( 14)
Simplify right-hand side
L=84π
L=263.893782...
L≈ 263.9
We know that the lateral area is 84π or approximately 263.9 m^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 84π and r with 3 into the formula, we can find S. Let's do it!
S=L+2π r^2
S= 84π+2π( 3)^2
Simplify right-hand side
S=84π+2π(9)
S=84π+18π
S=102π
S=320.442451...
S≈ 320.4
The surface area of the cylinder is about 320.4 m^2.