Question

A corn cob, shaped like a right circular cone, has the radius of its broadest end as $2.1cm$ and length (height) as $20cm$. If each $1{cm}^2$ of the surface of the cob carries an average of four grains, find the number of grains on the entire cob.

Answer 1

Radius of corn cob $=2.1cm$

Height of corn cob $=20cm$

Curved surface area $=\pi rl$

Now,

$l=\sqrt{r^2+h^2}=\sqrt{{\left(2.1\right)}^2+{\left(20\right)}^2}=\sqrt{404.41}l=20.11cm$

Therefore curved surface area of corn cob $=\frac{22}{7}\times 2.1\times 20.11=132.726c{m}^2$

Number of grains on $1c{m}^2=4$

Number of grains on $132.726c{m}^2=4\times 132.726=530.904=531$