Question

Find the volume of the cone for a cone having a slant height of 14 cm and radius of the base is 4 cm.​

Answer 1

Answer:

$slant \: height \: (l) = 14 \: cm \\ radius \: of \: base \: \: (r) = 4 \: cm \\ {l}^{2} = {r}^{2} + {h }^{2} \\ {14 }^{2} = {4}^{2} + {h}^{2} \\ 196 = 16 + {h}^{2} \\ 196 - 16 = {h }^{2} \\ {h }^{2} = 180 \\ h = \sqrt{180 } \: \: \: \: \: \: \: \: taking \: squre \: root \: \\ h = \sqrt{36 \times 5} \\ h = 6 \sqrt{5} \: cm \\ volume \: of \: cone \: = \frac{1}{3} \times \pi {r}^{2} h \\ \: \: \: = \frac{1}{3} \times \frac{22}{7} \times 4 \times 4 \times 6 \sqrt{5} \\ = 224.45 \: {cm}^{3} \\ voume \: of \: cone \: is \: 224.45 \: {cm}^{3}$