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

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

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

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

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

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

$\\ \sf\longmapsto r=\sqrt{0.71}$

$\\ \sf\longmapsto r=0.84in$

Answer 2

Answer:

Diameter is 3.00 inches

Step-by-step explanation:

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

${ \tt{volume = \pi {r}^{2} h}}$

• r is radius
• h is height

${ \tt{11.25\pi = \pi( {r}^{2} ) \times 5}}$

» Divide either sides by 5π

${ \tt{ \frac{11.25\pi}{ \green{5\pi}} = \frac{\pi {r}^{2} \times 5}{ \green{5\pi}} }} \\ \\ { \tt{2.25 = {r}^{2} }} \\ { \tt{ \sqrt{ {r}^{2} } = \sqrt{2.25} }} \\ { \tt{r = 1.5 \: in}}$

» From identical circular formulae, diameter is twice radius:

${ \boxed{ \tt{ \: diameter = 2 \times radius \: }}} \\ { \tt{d = 2 \times 1.5}} \\ { \tt{d = 3 \: inches}}$