Question

A bucket is in the form of a frustum of a cone with a capacity of $12408.8{cm}^3$ of water. The radii of the top and bottom circular ends are $20cm$ and $12cm$ respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use $\pi =3.14$)

Answer 1

Volume of frustum bucket $=12408.8{cm}^3$

$\Rightarrow \frac{1}{3}\pi h(R_1^2+R_2^2+R_1{R}_2)=12408.8{cm}^3=\frac{22}{3\times 7}\times h({20}^2+{12}^2+20\times 12)=12408.8$

$\Rightarrow h=\frac{12408.8\times 21}{22\times 784}\approx 15cm$

CSA of sheet $=\pi (R_1+R_2)l+\pi R_1^2=\pi (R_1+R_2)\sqrt{{(R_1-R_2)}^2+h^2}+\pi R_2^2$

$=3.14(20+12)\sqrt{{(20-12)}^2+{15}^2}+3.14\times {72}^2$

$=1708.16+452.16=2160.32{cm}^2$