Question

The volume of a right circular cone is 9856 cm³. Ifthe diameter of the base is 28 cm, find:
(i) height of the cone
(iii) curved surface area of the cone
(ii) slant height of the cone.

Answer 1

$\bf \large \it \: Hey \: User!!!$

given :-

• volume of the right circular cone = 9856cm³

• diameter of the base of the cone = 28cm

therefore radius of the cone = 28/2 (as we know that diameter is double of radius, hence radius will be the half if it's diameter)
= 14cm

according to the question, we have to answer three questions..

(i) height of the cone.

formula for the volume of a cone is 1/3πr²h

therefore 1/3πr²h = 9856cm³
>> 1/3 × 22/7 × 14 × 14 × h = 9856cm³
>> 22/3 × 2 × 14 × h = 9856cm³
>> 616/3 × h = 9856cm³
>> h = 9856/1 × 3/616
>> h = 16 × 3
>> h = 48cm

hence, the height of the cone is 48cm.

(ii) slant height of the cone.

as we know this is a right circular cone.

therefore slant height = √r²+h²
= √14²+48²
= √196+2304
= √2500
= 50cm

the slant height of the cone is 50cm.

(iii) curved surface area of the cone.

formula for the curved surface area of the cone is πrl.
l is the slant height of the cone.

hence it's curved surface area = πrl
= 22/7 × 14 × 50
= 22 × 2 × 50
= 2200cm²

$\bf \large \it{Cheers!!!}$