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

Explanation

We know that the grains of corn are found on the curved surface of the corn cob.
`:.` number of grains on the corn cob
= (curved surface area of the corn cob) `xx` (number of grains of corn on 1 `cm^(2)`)
So, we shall find the curved surface area of the corn cob.
We have, r = 2.1 cm and h = 20 cm
`:. l^(2) = r^(2) + h^(2) = (2.1)^(2) + (20)^(2) = 404.41`
So, `l sqrt(404.41) cm = 20.109 cm ~~ 20.11 cm`
Curved surface area of the corn cob
`= pi rl = ((22)/(7) xx 2.1 xx 20.11) cm^(2)`
`= 132.726 cm^(2) ~~ 132.73 cm^(2)`
Number of grains on `1 cm^(2) = 4`
`:.` number of grains on entire corn cob
`= (132.73 xx 4) = 530.92 ~~ 531`
So, there would be approximately 531 grains on the corn cob.