Question

If the radii of the circular ends of a conical bucket which is $32cm$ high are $40cm$ and $16cm$, find the capacity of total surface area of the bucket. $(Use\pi =\frac{22}{7})$.

Answer 1

Slant height $=L=\sqrt{h^2+(r_1-r_2{)}^2}$

$=\sqrt{1024+576}$

$=\sqrt{1600}=40$

$T.S.A=\pi l(r_1+r_2)+\pi r_1^2+\pi r_2^2$

$=\frac{22}{7}\times 40\left(56\right)+\frac{22}{7}\times 160+\frac{22}{7}\times 256$

$=\frac{22\times 2240}{7}+\frac{22\times 169}{7}+\frac{22\times 236}{7}$

$=\frac{49280+3520+5632}{7}$

$=\frac{56432}{7}$

$=8347.42c{m}^2$