Question

Determine the ratio of surface area to volume for each cylinder

Answer 1

2. The surface area of a cylinder is given by the following formula:

`SA=2\pi r^2+2\pi rh`

Where pi=3.14, r is the radius r=d/2, and h is the height.

And the volume of a cylinder is given by:

`V=\pi r^2h`

Where r is the radius r=d/2 and h is the height.

a. The given cylinder has a diameter d=18 cm (r = 18/2 = 9 cm) and a height h=7.5 cm.

Replace these values in the formulas and find the surface area and the volume:

`\begin{gathered} SA=2\pi(9)^2+2\pi(9)(7.5) \\ SA=2\pi\cdot81+2\pi\cdot67.5 \\ SA=508.9cm^2+424.1cm^2 \\ SA=933cm^2 \\ V=\pi(9)^2(7.5) \\ V=\pi\cdot81\cdot7.5 \\ V=1908.5cm^3 \end{gathered}`

The ratio of surface area to volume is then:

`(SA)/(V)=(933cm^2)/(1908.5cm^3)=0.5`

b. The given cylinder has a radius r = 5 cm and a height h=23 cm.

Replace these values in the formulas and find the surface area and the volume:

`\begin{gathered} SA=2\pi(5)^2+2\pi(5)(23) \\ SA=2\pi\cdot25+2\pi\cdot115 \\ SA=157.1cm^2+722.6cm^2 \\ SA=879.6cm^2 \\ V=\pi(5)^2(23) \\ V=\pi\cdot25\cdot23 \\ V=1806.4cm^3 \end{gathered}`

The ratio of surface area to volume is then:

`(SA)/(V)=(879.6cm^2)/(1806.4cm^3)=0.5`