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=2Ï€ 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=2Ï€ rh
L=2Ï€( 3)( 14)
â–¼
Simplify right-hand side
L=84Ï€
L=263.893782...
L≈ 263.9

We know that the lateral area is 84Ï€ or approximately 263.9 m^2.

Surface Area

To calculate the surface area of a cylinder, we can use the following formula. S=L+2Ï€ r^2 In this formula, L is the lateral area of the cylinder and r is the radius of the base. Substituting L with 84Ï€ and r with 3 into the formula, we can find S. Let's do it!

S=L+2Ï€ r^2
S= 84Ï€+2Ï€( 3)^2
â–¼
Simplify right-hand side
S=84Ï€+2Ï€(9)
S=84Ï€+18Ï€
S=102Ï€
S=320.442451...
S≈ 320.4

The surface area of the cylinder is about 320.4 m^2.