Question

Twenty meters of wire is available for fencing off a flowerbed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is ______

Options

• 30

• 12.5

• 10

• 25

Answer 1

Twenty meters of wire is available for fencing off a flowerbed in the form of a circular sector. Then the maximum area (in sq. m) of the flowerbed, is 25.

Explanation:

 

Total length of wire = r + r + rθ

⇒ 20 = 2r + rθ

⇒ θ = `(20 - 2r)/r`

A = `1/2r^2theta`

= `1/2r^2((20 - 2r)/r) = 10r - r^2`

∴ `(dA)/(dr)` = 10 - 2r

For maximum area, `(dA)/(dr)` = 0

⇒ 0 = 10 - 2r ⇒ 10 = 2r ⇒ r = 5 m

∴ Area = `1/2r(20 - 2r)`

= `1/2 xx 5 xx (20 - 10) = 25` sq.m.