Question

A cylindrical soup can is 5 inches tall and contains 11.25π cubic inches of soup. What is the diameter of the can to the nearest hundredth of an inch?

Answer 1

Diameter is 3.00 inches

Explanation:

» Volume of a cylindrical soup is given a formula below:

`{ \tt{volume = \pi {r}^(2) h}}`

• r is radius
• h is height

`{ \tt{11.25\pi = \pi( {r}^(2) ) * 5}}`

» Divide either sides by 5π

`{ \tt{ \frac{11.25\pi}{ \green{5\pi}} = \frac{\pi {r}^(2) * 5}{ \green{5\pi}} }} \\ \\ { \tt{2.25 = {r}^(2) }} \\ { \tt{ \sqrt{ {r}^(2) } = √(2.25) }} \\ { \tt{r = 1.5 \: in}}`

» From identical circular formulae, diameter is twice radius:

`{ \boxed{ \tt{ \: diameter = 2 * radius \: }}} \\ { \tt{d = 2 * 1.5}} \\ { \tt{d = 3 \: inches}}`

Answer 2

• Radius be r
• h=5in
• Volume=V=11.25πin^3

`\\ \sf\longmapsto V=\pi r^2h`

`\\ \sf\longmapsto 11.25=5\pi r^2`

`\\ \sf\longmapsto 2.25=\pi r^2`

`\\ \sf\longmapsto r^2=2.25/3.14=0.71`

`\\ \sf\longmapsto r=√(0.71)`

`\\ \sf\longmapsto r=0.84in`