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Question

# Determine which has the greater effect on the surface area of a cylinder: doubling the base radius or doubling the height. Justify.

Solution

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The lateral area of a prism is the product of the perimeter of the base and the height.

$LA=ph$

where $p$ is the perimeter of the base and $h$.

The surface area of a prism is the sum of the lateral area and the areas of the two bases.

$SA=LA+2B$

where $B$ is the area of the base.

Given:

$b=4 \text{ \ in}$

$h=7 \text{ \ in}$

$h'=3 \text{ \ in}$

$a=5 \text{ \ in}$

Perimeter is

$p=5+4+3 \text{ \ in}=12 \text{ \ in}$

So,

$LA=ph=12 \times 7 \text{ \ in}^2=84 \text{ \ in}^2$

Area of the triangle is

$A=\frac{1}{2} \times b \times h'$

where $b$ is the base of the triangle and $h$ is the height of the triangle.

So,

$B=\frac{1}{2} \times b \times h'=\frac{1}{2} \times 4 \times 3 \text{ \ in}^2=6 \text{ \ in}^2$

Hence,

$SA=LA+2B=84+2 \times 6 \text{ \ in}^2=96 \text{ \ in}^2$

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