Question

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

Answer 1

Given:

Radius of base, r = 2.1 cm

Height, h = 20 cm

Average grains per cm² = 4

Slant height of a right circular cone: l = `sqrt(h<sup>2</sup> + r<sup>2</sup>).`

Curved (lateral) surface area of a cone: A = π r l.

Total grains = surface area in cm² × grains per cm².

Compute slant height: l = `sqrt(h^2 + r^2)`

= `sqrt(202 + 2.12)`

= `sqrt(400 + 4.41)`

= `sqrt(404.41)`

= 20.11 cm.

Curved surface area:

A = π r l = 3.14 × 2.1 × 20.11

= 3.14 × 42.231

= 132.61 cm².

Number of grains:

Total grains = A × 4

= 132.61 × 4

= 530.44

= 530 grains