[tex]\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}[/tex]
Answer:
volume of a cone is
[tex] \frac{1}{3} \pi \: {r}^{2} h[/tex]
[tex]taking \: \pi \: as \: 3.142[/tex]
[tex]59 = \frac{1}{3} \times 3.142 \times {2.5}^{2} \times h[/tex]
[tex]59 \times 3 = 3.142 \times 6.25 \times h[/tex]
[tex]177 = 19.6375h[/tex]
[tex]177 \div 19.6375 = 19.6375 h \div 19.6375[/tex]
h=19.013
to the nearest hundredths
h=19.0
