Question

What is the value of the ratio of the surface area to the volume of the cylinder.

A cylinder has a radius of 4 ft and a height of 12 ft.

A. 0.39
B. 0.82
C. 1.5
D. 0.67

Answer 1

`\bf \textit{total surface area of a cylinder}\\\\ SA=2\pi r(h+r)~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=4\\ h=12 \end{cases}\implies SA=2\pi (4)(12+4) \\\\\\ SA=8\pi (16)\implies SA=128\pi \\\\ -------------------------------\\\\ \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=4\\ h=12 \end{cases}\implies V=\pi (4)^2(12)\implies V=192\pi`


`\bf -------------------------------\\\\ \cfrac{SA}{V}\qquad \qquad \cfrac{128\pi }{192\pi }\implies \stackrel{simplified}{\cfrac{2}{3}}`

Answer 2

Correct option is C.

Explanation:

Given the radius and height of cylinder. we have to find out the ratio of surface area to the volume of the cylinder.

Radius=4 ft

Height=12 ft

`\text{Surface Area of cylinder=}2\pi r(r+h)=2\pi 4(4+12)=128\pi ft^2`

`\text{Volume of cylinder=}\pi r^2h=\pi (4^2)(12)=192\pi ft^2`

`Ratio=(Surface area)/(volume)`

=
`(128)/(192)=0.67ft^2`

Hence, correct option is C.