Question

A reservoir in the form of the frustum of a right circular cone contains $44\times {10}^7$ litres of water which fills it completely. The radii of the bottom and top of the reservoir are $50$ metres and $100$ metres respectively. Find the depths of water and the lateral surface area of the reservoir. (Take $\pi =22/7$)

Answer 1

Volume of frustum cone $=44\times {10}^{7}litre=44\times {10}^4{m}^3$

$\Rightarrow \frac{1}{3}\pi h(R_1^2+R_2^2+R_1{R}_2)=44\times {10}^4\Rightarrow \frac{1}{3}\times \frac{22}{7}\times h=\frac{44\times {10}^4\times 3\times 7}{22\times 17500}=24m$

$\Rightarrow \frac{1}{3}\times \frac{22}{7}\times h(10000+2500+5000)=44\times {10}^4\Rightarrow h=\frac{44\times {10}^4\times 3\times 7}{22\times 17500}=24m$

slant height $\left(l\right)=\sqrt{{(R_1-R_2)}^2+h^2}=\sqrt{{(100-50)}^2+{\left(24\right)}^2}=\sqrt{2500+576}=55.46m$

$CSA=\pi (R_1+R_2)l=\frac{22}{7}(100+50)\times 55.46=26145.43m^2$