Exercise 38 Page 820

Table:

Cylinder	A	B	C
Radius	r=3	r=6	r=3
Height	h=5	h=5	h=10
Lateral Area	L_\text{A}=30\pi	L_\text{B}=60\pi	L_\text{C}=60\pi
Surface Area	S_\text{A}=39\pi	S_\text{B}=96\pi	S_\text{C}=69\pi

Practice makes perfect

We are asked to draw three cylinders with the following dimensions.

Cylinder	A	B	C
Radius	r=3	r=6	r=3
Height	h=5	h=5	h=10

Let's do it!

We are asked to create a table of the radius, height, lateral area, and surface area of cylinders A, B, and C. Let's do it!

Cylinder	A	B	C
Radius	r= 3	r= 6	r= 3
Height	h = 5	h = 5	h = 10
Lateral Area	L=2π r h
Lateral Area	L_\text{A}=2\pi ({\color{#0000FF}{3}})({\color{#009600}{5 }})=30\pi	L_\text{B}=2\pi ({\color{#0000FF}{6}})({\color{#009600}{5 }})=60\pi	L_\text{C}=2\pi ({\color{#0000FF}{3}})({\color{#009600}{10}})=60\pi
Surface Area	S=2π r h +π r^2
Surface Area	S_\text{A}=2\pi ({\color{#0000FF}{3}})({\color{#009600}{5 }})+\pi({\color{#0000FF}{3}})^2=39\pi	S_\text{B}=2\pi ({\color{#0000FF}{6}})({\color{#009600}{5 }})+\pi({\color{#0000FF}{6}})^2=96\pi	S_\text{C}=2\pi ({\color{#0000FF}{3}})({\color{#009600}{10}})+\pi({\color{#0000FF}{3}})^2=69\pi

Based on the table from Part B, if we double the radius or the height of Cylinder A we double its lateral area. If we double the radius or the height of Cylinder A, the surface area is increased, but not proportionally. This happens because the lateral area L=2π rh varies directly with r and h, while the surface area does not.

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