Question

A cylindrical bucket of diameter $28cm$ and height $20cm$ was full of sand. When the sand in the bucket was poured on the ground, the sand got converted into a shape of a cone. If the height of the cone was $14cm$, what was the base area of the cone ?

Answer 1

We have,

Cylindrical bucket of diameter $=28cm.$

Then, radius$r=\frac{28}{2}=14cm.$

Height of cylindrical bucket$=14cm.$

Now,

Volume of cylinder$=\pi r^{2}h$

$=\pi 14\times 14\times 14$

$={14}^3\pi$

So,

Height of cone $h=14cm.$

Radius $r=?$

But according to given question,

Volume of cylinder=Volume of cone

${14}^3\pi =\frac{1}{3}\pi r^{2}h$

$\frac{1}{3}\pi r^2\times 14=\pi 14\times 14\times 14$

$r^2=14\times 14\times 3$

$r=14\sqrt{3}cm.$

Now, Base area of cone$=\pi r^2$

$=\frac{22}{7}\times 14\times 14\times 3$

$=22\times 14\times 6$

$=1848c{m}^2$

Hence, this is the answer.