Question

A corn cob, shaped somewhat like a cone, has the radius of ITS broadcast end is is 2.1cm and length as 20cm. If each 1cm² of the surface of the cop carries an average of 4 grains, find how many grains you would find on the entire cob?

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Answer 1

$\sf \large GIVEN :$

A corn cob, shaped somewhat like a cone, has the radius of it's broadcast end is 2.1cm and length as 20cm. If each 1cm² of the surface of the cop carries an average of 4 grains, find how many grains you would find on the entire cob?

$\sf \large \: SOLUTION : \:$

••• Since the grains of corner found only on the curved surface of the corn cob, we would need to know the curved surface area of the corn cob to find the total number of grains on it. In this question, we are given the height of the cone, so we need to find its slant height. •••

Here,

$\sf l = \sqrt{r {}^{2} + h {}^{2} } \\ \: \: \: = \sqrt{(2.1 {)}^{2} + 2 {0}^{2} } \\ \: \: \: = \sqrt{404.41} cm \: = \: 20.11cm$

→ Therefore, the curved surface area of the corn cob = $πrl$

= $\ sf\frac{22}{7}$ × 2.1 × 20.11cm² = 132.726cm² = 132.73cm² (approx.)

✓ Number of grains of corn on 1cm² of the surface of the corn cob = 4

→ Therefore, number of grains on the entire curved surface of the cob = 132.73 × 4 = 530.92 = 531 (approx.)

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

- TwinklingStar