39, A right circular cone of radius 3 cm, hasa curved surface area of

1.	39, A right circular cone of radius 3 cm, hasa curved surface area of 47.1 cm2. Findthe volume of the cone. (Use Ď3.14)(24Âˇ60cm"CBSE 2016]
Answer» GIVEN: Radius of cone ( r ) = 3 cm, Curved surface area of a cone= 47.1 cm²Curved surface area of a cone= πrl 47.1 = πrl47.1 = 3.14 × 3 × ll = 47.1 / (3.14 × 3)l = 15.7 / 3.14= 1570/314= 5 cm slant height (l) = 5 cm Height of a cone (h) = √(l²) - (r²)h = √ 5² -3²h = √ 25 - 9 = √ 16 = 4 cmh = 4 cm Volume of cone= ⅓(πr²h)= ⅓(3.14 × 3 × 3 × 4)= 3.14 × 12= 37.68 cm³ Hence, the volume of a cone is 37.68 cm³.

39, A right circular cone of radius 3 cm, hasa curved surface area of 47.1 cm2. Findthe volume of the cone. (Use Ď3.14)(24Âˇ60cm"CBSE 2016]

Answer»

GIVEN:

Radius of cone ( r ) = 3 cm,

Curved surface area of a cone= 47.1 cm²Curved surface area of a cone= πrl

47.1 = πrl47.1 = 3.14 × 3 × ll = 47.1 / (3.14 × 3)l = 15.7 / 3.14= 1570/314= 5 cm

slant height (l) = 5 cm

Height of a cone (h) = √(l²) - (r²)h = √ 5² -3²h = √ 25 - 9 = √ 16 = 4 cmh = 4 cm

Volume of cone= ⅓(πr²h)= ⅓(3.14 × 3 × 3 × 4)= 3.14 × 12= 37.68 cm³

Hence, the volume of a cone is 37.68 cm³.