Question

The radii of the circular ends of a frustum of a cone are 33 cm and 27 cm, and

its slant height is 14 cm. find the curved surface area of the frustum of a cone.​

Answer 1

Step-by-step explanation:

The radius of circular ends of a solid frustum of a cone are 33 cm and 27 cm.

So, suppose R = 33 cm and r = 27 cm and slant height; l = 10 cm

Now we know that slant height of frustum, l = h2+(R−r)2‾‾‾‾‾‾‾‾‾‾‾‾√ where h is the height of frustum

10 = h2+(33−27)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√⇒102 = h2+36⇒h2 = 100−36 = 64⇒h = ±64‾‾‾√ = ±8

As the height can't be negative so neglect h = -8.

So, h = 8 cm

So, volume of frustum = πh3(R2+r2+Rr) = 227×83(332+272+33×27) = 227×83×2709 = 22704 cm3

And total surface area of frustum = π[R2+r2+l(R+r)] = 227[332+272+10(33+27)] =