Answer:
The radius of the cone is 21 units
The volume of the cone is 9702 units³
Explanation:
* Lets revise the area of the circle and the volume of the cone
- The base if the cone is a circle
- The area of the circle is πr², where r is the radius of the circle
∵ The area of the base of the cone = 1386 units²
∵ The area of the base = πr²
∵ π = 22/7
∴ 1386 = 22/7 (r²) ⇒ multiply each side by 7
∴ 9702 = 22 r² ⇒ divide both sides by 22
∴ 441 = r² ⇒ take √ for both sides
∴ 21 = r
* The radius of the cone is 21 units
- The volume of the cone = 1/3 πr²h , where h is the height of the cone
∵ The cone's height is equal to the radius of its base
∴ h = r
∵ The volume of the cone = 1/3 πr²h
∴ The volume of the cone = 1/3 πr²(r) = 1/3 πr³
∵ r = 21 units
∴ The volume of the cone = 1/3 (22/7) (21)³
∴ The volume of the cone = 9702 unit³
* The volume of the cone is 9702 units³