Question

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

Answer 1

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  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,

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

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

Answer 2

$\bf\underline{\underline{\pink{Question:-}}}$

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

$\bf\underline{\underline{\blue{Solution:-}}}$

We know that the grains of corn are found on the curved surface of the cone cob.

∴ number of grains on the corn cob = (curved surface area of the corn cob)×(numbers of grains of corn on 1 cm²)

So, we shall find the curved surface area of the corn cob.

We have, r = 2.1cm and h = 20cm.

∴ l² = r² + h² =(2.1)² + (20)² = 404.41

So, l = √404.41 cm = 20.109 cm = 20.11 cm

Curved surface area of the corn cob = πrl = ( $\frac{22}{7}$×2.1×20.11 ) cm²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ = 132.726 cm² ≈ 132.76 cm²

Number of grains on 1cm² = 4

∴ number of grains on entire corn cob = (132.76 × 4)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ = 530.92 ≈ 531

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

$\bf\underline{\underline{\green{Extra\: Fomulae:-}}}$

★For a right circular cone of radius = r units, height = h and the slant height = l units, we have

☙Slant height of the cone(l) = √h²+r² units

☙Volume of the cone = ⅓πr²h cubic units

☙Area of curved surface = (πto) sq units = (πr√h²+r²) sq units

☙Total surface area = (area of the curved surface) + (area of base)

= (πrl+πr²) sq units = πr(l+r) sq units

$\bf\underline{\underline{\orange{Extra\: Information:-}}}$

☙The solid generated by the rotation of a right-angled triangle about one of the sides containing the right angle is called a right circular cone.