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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