Question

Find the height of the can in inches. Round your answer to the nearest tenth if necessary.(Info in image)

Answer 1

Given data:

circumference of a cylinder = 3 3/4

volume of the cylinder = 7.

to find the height of the cylinder.

Use the formula,

`v=\pi\cdot((c)/(2\pi))^2\cdot h`

subsitute the values in the formula,

`\begin{gathered} 7=\pi\cdot(((15)/(4))/(2\pi))^2\cdot h \\ 7=(22)/(7)\cdot(((15)/(4))/(2\cdot(22)/(7)))^2\cdot h \\ 7=(22)/(7)\cdot((15)/(8\cdot(22)/(7)))^2\cdot h \\ (22\cdot\:15^2)/(7\cdot\:8^2\cdot(22^2)/(7^2))\cdot h=7 \\ (15^2\cdot\:22)/((30976)/(7))\cdot h=7 \\ (22\cdot\:15^2\cdot\:7)/(30976)\cdot h=7 \\ (15^2\cdot\:7)/(1408)\cdot h=7 \\ (1575)/(1408)\cdot h=7 \\ 1575h=9856 \\ h=(1408)/(225) \\ h=6.25 \end{gathered}`

The height of the cylinder is 6.3 in.