A cone of height 8 m has a curved surface area 188.4 square metres.Fin

1.	A cone of height 8 m has a curved surface area 188.4 square metres.Find its volume. (Take Tt 3.14.)
Answer» 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 m^2 pirl = 188.4 On squaring both sides, we get r^4 + 100 r^2-36r^2 -3600 = 0 r^2(r^2 + 100) -36 (r^2 + 100) = 0 (r^2-36)(r^2+100) = 0 r^2 = 36, -100 r^2 ≠ -100 r^2 = 36 or r = 6 cm Hence radius is 6 cm. Now volume of the cone = (1/3)pir^2h= (1/3)pi6^2h= (3.41368)/3= 3.41128= 301.44 cm^3

A cone of height 8 m has a curved surface area 188.4 square metres.Find its volume. (Take Tt 3.14.)

Answer»

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 m^2

pi*r*l = 188.4

On squaring both sides, we get

r^4 + 100 r^2-36r^2 -3600 = 0

r^2(r^2 + 100) -36 (r^2 + 100) = 0

(r^2-36)(r^2+100) = 0

r^2 = 36, -100

r^2 ≠ -100

r^2 = 36

or r = 6 cm

Hence radius is 6 cm.

Now volume of the cone = (1/3)*pi*r^2*h= (1/3)*pi*6^2*h= (3.41*36*8)/3= 3.41*12*8= 301.44 cm^3