Question

a cone has a base area of 20m square and volume of 160 m cube.find the height of the cone​

Answer 1

$\sf{\large{\underline{\underline{EXPLANATION:}}}}$

★Given,,

• Area of base of cone,πr²=20m²
• Volume of the cone,⅓πr²h=160m³

★To find,,

• Height of the cone,h=??

★Since we know,,

Area of base of cone,,

$\pi \: r {}^{2} = 20 \\ = > {r}^{2} = \frac{20}{\pi} \\ = > r = \sqrt{ \frac{20}{\pi} } m$

Volume of the cone,,

$\frac{1}{3} \pi \: r {}^{2} h = 160 \\ = > \frac{1}{3} \pi \: \times (\sqrt \frac{20}{\pi} ) {}^{2} h = 160 \\ = > \frac{\pi}{3} \times \frac{20}{\pi} \times h = 160 \\ = > \frac{20h}{3} = 160 \\ = > h = \frac{160 \times 3}{20} \\ = > h = 24m$

★Therefore,,

Height of the cone,h=24m

$\rule{200}2$

❣️❣️★Hope it helps★❣️❣️