Question

A tree is surrounded by barriers . For each inch of the trunk diameter the protection zone should have a radius 1/1/3 feet . Find the area of the zone for the tree with a trunk circumference of 63 inches

Answer 1

The area of the zone for the tree with a trunk circumference of 63 inches will be 2124.57 sq. inches.

We know, the circumference of a circle with radius 'r' is given as 2πr.

Given that, circumference = 63 inches

So, 2Пr = 63

⇒2×(22/7)×r = 63           [П = 22/7]

⇒ (44r/7) = 63

r = 441/44 = 10.02

r ≈ 10 inches

Given, radius of the zone = 1 1/3 feet = 4/3 feet = (4×12)/3 = 16 inches.  [As 1 feet = 12 inches]

Now, the radius of the zone will be = (10 + 16) inches = 26 inches

We know, for a circle with radius 'r', its area will be Пr²

So, area of zone with 26 inches radius is:

= 22/7×26×26

= 14872/7 =2124.57 sq inches.

Area of the zone = 2124.57 sq inches.