Question

A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm². Find the volume of the cone.(use π= 3.14)
(Class 10 Maths Sample Question Paper)

Answer 1

Solution:
GIVEN:

Radius of cone ( r ) = 3 cm,

Curved surface area of a cone= 47.1 cm²
Curved surface area of a cone= πrl

47.1 = πrl
47.1 = 3.14 × 3 × l
l = 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 -3²
h = √ 25 - 9 = √ 16 = 4 cm
h = 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.

HOPE THIS WILL HELP YOU...

Answer 2

Hi Friend ✋✋✋

Radius of Cone = 3cm

CSA of Cone = πrl = 47.1 cm²

22/7 × 3 × l = 47.1

l = 47.1 × 7 / 22 × 3

l = 15.7 × 7 / 22

l = 109.9 / 22

l = 4.995 cm

h² = l² - r²

h² = 24.95 - 9

h = √ 15.95

h = 3.99 cm

Volume of Cone = ⅓πr²h

= 1/3 × 22/7 × 3 × 3 ( 3.99 )

= 22 × 3 × 3.99 / 7

= 263.34/7

= 37.62 cm³

Hope it Helps