Question

A corn cob, shaped somewhat like a cone, has the radius of its broadest end as $2.1cm$ and length (height) as $20cm$. If each $1c{m}^2$ of the surface of the cob carries an average of four grains, find how many grains (approximately) you would find on the entire cob.

• A. $511$
• B. $531$
• C. $551$
• D. $571$

Answer 1

The correct option is B $531$

We know, the curved surface area of cone cob = $\pi rl$.

Given, $r=2.1cm,h=20cm$.

Now, slant height $l=\sqrt{r^2+h^2}=\sqrt{{\left(2.1\right)}^2+{\left(20\right)}^2}$

$⟹$ $l=\sqrt{404.41}=20.11cm$

$\therefore$ Curved surface area of corn cab = $\frac{22}{7}\times 2.1\times 20.11=132.73{cm}^2$.

Since, the number of grains on $1$ ${cm}^2$ of the surface corn cob $=4$,

$\therefore$ Number of grain on $132.73$ ${cm}^2$ of the surface of corn cab $=132.73$$\times 4=530.92\approx 531$.

Hence, option $B$ is correct.