Question

A cone of height 8m has a curved surface area 188.4 square metres. find its volume

Answer 1

Given, height of cone, h = 8 m

Let r be radius and l be slant height of cone,

Given, curved surface are of cone = 188.4 m2

⇒ πrl = 188.4

On squaring both sides, we get

r4 + 100 r2-36r2 -3600 = 0

r2(r2 + 100) -36 (r2 + 100) = 0

(r2-36)(r2+100) = 0

⇒ r2 = 36, -100

 r2 ≠   -100

⇒ r2 = 36

or r = 6 cm

Hence radius is 6 cm.

Answer 2

Given:

1. height of a cone is h

so that,

h=8m

let assume r is the radius and L is the tilt height or length of a cone.

2. curved surface are of cone is A,

so that ,

A= 188.4 square meters

r=root(A²/(pi*(pi*h²+2A)))

r=root(188.4²/(pi*(pi*8²+2(188.4)))

r=4.42 m

volume of a cone can be given as,

V=pi*r²*h/3

V=pi*(4.42)²*8/3

V=163.66 cubic metres