Question

A corn cob, shaped like a cone, has the radius of its broadest end as 1.4 cm and length (height) as 12 cm 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) 211
B) 212
C) 213
D) 214

Answer 1

Hint:
It is given that r = 1.4 cm and h = 12 cm.
Now, using the formula $l=\sqrt{r^2+h^2}$, find l of the cone.
Thus, find the area of the cone by $A=\pi rl$.
Finally, $A\times 4$ will give the number of corn grains in the entire cob.

Complete step by step solution:
Here, it is given that the radius of its broadest end is 1.4 cm and length (height) as 12 cm of the surface of the cob.
Thus, r = 1.4 cm and $$h=12$$ cm.

So, we get l using the formula $l=\sqrt{r^2+h^2}$ .
 $\therefore l=\sqrt{{\left(1.4\right)}^2+{\left(12\right)}^2}$
       $$\begin{gathered} =\sqrt{1.96+144} \\ =\sqrt{145.96} \\ =12.08 \end{gathered}$$
The C.S.A. of the cone is given by $A=\pi rl$ .
 $$\begin{gathered} \therefore A=\pi \left(1.4\right)\left(12.08\right) \\ ={\displaystyle \frac{22}{7}}\left(1.4\right)\left(12.08\right) \\ =53.15 \\ =53.2c{m}^2 \end{gathered}$$
Thus, the area of the cone cob is $53.2c{m}^2$.
It is also given that, number of corn grains in the $1c{m}^2$ area is 4.
Thus, the number of corn grains carried in $53.2c{m}^2$ is $53.2\times 4=212.8=213$ approximately.

So, option (C) is correct.

Note:
Here, the number 53.15 is rounded to 53.2 because the second digit after the decimal is 5, and if the digit after decimal is greater than or equal to 5 we add +1 to the previous digit i.e. 1 after the decimal.
Similarly, 212.8 is rounded off to 213, because the digit after decimal is greater than 5 i.e. 8, so we add +1 to 212 = 213.