Q3 of 44 Page 15

The radii of the circular ends of a solid frustum of a cone are 33 cm and 27cm, and its slant height is 10cm. Find its capacity and total surface area. [Take π=22/7]


Greater radius = R = 33 cm


Smaller radius = r = 27 cm


Slant height = l = 10 cm


Total Surface area of the frustum = πR2 + πr2 + πl(R+r)


= π[(33)2 + (27)2+ 10×(33+27)]


= π[1089 + 729 + 600]



= 7599.428 cm2


= 7599.43 cm2


We first need to find the height, h


l2 = (R – r)2 + h2


⇒ (10)2 = (33 – 27)2 + h2


⇒ 100 = (6)2 + h2


⇒ 100 = 36 + h2


⇒ h2 = 100 – 36


⇒ h2 = 64


⇒ h = ±8


⇒ h = 8cm


Now, Capacity of a solid frustum of a cone = Volume of frustum






= 22704 cm3


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