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 sq cm of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob? [4 MARKS]

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Solution

Formula: 1 Mark each
Application: 2 Marks

$r = 2.1, h = 20$

Total number of grains on the corn cob = 4 Curved surface area of the corn cob

$l = \sqrt{r^{2} + h^{2}}$

$= \sqrt{{2.1}^{2} + 20^{2}}$

$= 20.11$

Curved surface area
$= π r l$

$= \frac{22}{7} \times 2.1 \times 20.11$

$= 132.73 c m^{2}$

Total number of grains on the corn cob
$= 132.73 \times 4 = 530. 92$

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

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