Question

A cone with a radius of 2.5 cm is shown.its volume is 59 cubic centimeters. Enter the height of the cone.round your answer to the nearest hundreth

Answer 1

volume of a cone is

`(1)/(3) \pi \: {r}^(2) h`

`taking \: \pi \: as \: 3.142`

`59 = (1)/(3) * 3.142 * {2.5}^(2) * h`

`59 * 3 = 3.142 * 6.25 * h`

`177 = 19.6375h`

`177 / 19.6375 = 19.6375 h / 19.6375`

h=19.013

to the nearest hundredths

h=19.0

Answer 2

`\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=2.5\\ V=59 \end{cases}\implies \begin{array}{llll} 59=\cfrac{\pi (2.5)^2 h}{3}\implies (3)59=6.25\pi h \\\\\\ \cfrac{(3)59}{6.25\pi }=h\implies 9.01\approx h \end{array}`