Question

the radius and slant height of a cone are in the ratio 3:5 and its curved surface area is 423.9cm^2. find the volume of the cone. (π=3.14)​

Answer 1

Answer:

Volume = 3052.08 cm³

Step-by-step explanation:

Curved surface area = 423.9 cm²

Given,

Radius of cone and slant height are in ratio 3 : 5

Let the common ratio be  x

So,

radius of cone = 3x

Slant height = 5x

We know,

Curved Surface area = π * r * l

where r is radius and l is slant height.

Substituting the values,

423.9 = 3.14 * 3x * 5x

423.9 = 47.1 * x²

423.9 / 47.1 = x²

9 =x²

x = 3

So,

radius = 3x = 3*3 = 9 cm

Slant height = 5x = 5*3 = 15 cm

We also know ,

l²= r ² + h²

Substituting the values,

225 = 81 + h²

225 - 81 = h ²

144 = h ²

h = √ 144

h = 12 cm

We know,

Volume = π * r² * h

Volume = 3.14 * 9² * h

Volume = 3052.08 cm³