Question

find the value of a cone, if its total surface area is 7128 sq cm and the radius of base is 28cm. (π=22/7).​

Answer 1

Answer:

S.A. = πr(r+l) = 7128

3.14*28*(28+l) = 7128

l = 53 cm.

now volume

V = 1/3* π*r^2*l

= 1/3 *3.14*(28)^2*53

V = 43491 square cm.

Answer 2

Let the perpendicular height and the slant height be (h cm) and (l cm ) respectively. Radius of the base cone/r=28cm. Total Surface Area=7128sq.cm. pi*r (r+l)=7128 sq.cm => 22/7 *28(28+l)=7128. => 28+l=7128/22*4. => l=81-28. => l=53cm. Now, (r)^2 + (h)^2 = (l)^2. => (28)^2 + (h)^2 = (53)^2. => (h)^2 = 2809-784. => (h)^2 = 2025. => h = root 2025. => h = 45cm. Volume of the cone = 1/3 pi*r^2*h. => 1/3*22/7*(28)^2*45. => 36960 cube.cm So, Volume of the cone = 36960 cm.cube