Question

A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length as 20 cm. If each 1 cm2 of the surface of the cob carries an average of four grains, then find how many grains you would find on the entire cob?

Answer 1

Answer:

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Answer 2

AnswEr:

Since the grains of corn are found on the curved surface of the corn cob.

So, Total number of grains on the corn cob

= Curved surface area of the corn cob $\times$ Number of grains of corn on 1 cm².

Now, we will first find the curved surface area of the corn cob

We have , r = 2.1 and h = 20

Let l be the slant height of the conical cob. Then,

$\sf \: l = \sqrt{ {r}^{2} + {h}^{2} } = \sqrt{ {(2.1)}^{2} + {(20)}^{2} } \\ \\ = \sf\sqrt{4.41 + 440} = \sqrt{404.14} = 20.11 \\ \\ \therefore \: \sf \: curved \: surface \: area \: = \pi rl \\ \\ = \sf \: \frac{22}{7} \times 2.1 \times 20.11 \: {cm}^{2} \\ \\ = \sf \: 132.73 \: {cm}^{2}$

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Hence, Total number of grains on the corn cob = 132.73 $\times$ 4 = 530.92

So, there would be approximately 531 grains of corn on the cob.