Chapter 12.2, Problem 38PPS

(a)

To determine

To graph: To sketch 3 different cylinders.

Explanation of Solution

Concept used:

A cylinder is a three dimensional solid that has two parallel (usually circular) bases connected by a curved surface.

Graph:

Three cylinders A, B and C of different dimensions are drawn below

A.

  

B.

  

C.

  

Interpretation:

In the figure (A) radius of the circular base is 2 cm and height is 3 cm

In the figure (B) radius of the circular base is 2 cm and height is doubled, h = 6cm

In the figure (C) radius of the circular base is doubled, r = 4 cm and height is 3 cm

(b)

To determine

To tabulate: To create a table consisting of lateral area and surface areas of 3 cylinders.

Explanation of Solution

Formula used:

Lateral surface area of cylinder = $2\pi rh$

Total surface area of cylinder =lateral area + 2(base area)

= $2\pi rh+2\pi r^2$

Table:

A table consisting of radius, height, lateral area and surface area of cylinders A, B and C drawn in part (a) is created below.

Name ofcylinder	Radius, r	height, h	Lateral area	Surface Area
A	2	3	$2\pi \cdot 2\cdot 3=12\pi$$$	$12\pi +2\left(\pi \cdot 2^2\right)=20\pi$
B	2	6	$2\pi \cdot 2\cdot 6=24\pi$	$24\pi +2\left(\pi \cdot 2^2\right)=32\pi$$$$$
C	4	3	$2\pi \cdot 4\cdot 3=24\pi$	$24\pi +2\left(\pi \cdot 4^2\right)=56\pi$$$

(c)

To determine

To interpret: To interpret the results in part (b)

Explanation of Solution

Given information:The radius, height, lateral area and surface area of cylinders A, B and C are tabulated in part (b)

From the table in part (b) we notice that:

• When the radius is doubled (comparing 2^nd and 4^th row) the lateral area doubles as well. While the surface area increases but not proportionally.
• When the height is doubled (comparing 2^nd and 3^rd row) the lateral area doubles as well. While the surface area increases but not proportionally.

This happens because the lateral area varies directly with r and h, while the surface area doesn’t.