McGraw Hill Glencoe Geometry, 2012
MH
McGraw Hill Glencoe Geometry, 2012 View details
Mid-Chapter Quiz
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Exercise 10 Page 872

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

Lateral Area: 1131.0 in^2
Surface Area: 1639.9 in^2

Practice makes perfect

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. We know that the diameter d of the base is equal to 18inches and is exactly twice as long as its radius. d=2r ⇒ r= d2= 182=9in. Substituting r with 9 and h with 20 into the formula, we can find L.

L=2Ï€ rh
L=2Ï€( 9)( 20)
â–¼
Simplify right-hand side
L=360Ï€
L=1130.973355...
L≈ 1131.0

We know that lateral area is 360Ï€ or about 1131.0 in^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 720Ï€ and r with 9 into the formula, we can find S. Let's do it!

S=L+2Ï€ r^2
S= 360Ï€+2Ï€( 9)^2
â–¼
Simplify right-hand side
S=360Ï€+2Ï€(81)
S=360Ï€+162Ï€
S=522Ï€
S=1639.911365...
S≈ 1639.9

The surface area of the cylinder is about 1639.9 in^2.