A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.
For frustum:
Base radius, r’ = 20/2 = 10cm
Top radius, r’’ = 12/2 = 6cm
Height, h = 3cm
Volume =
= 616 cub. cm
Let l be the slant height of the cone, then
⇒ l = 5cm
Total surface area of the frustum = π (r’ + r’’) × l + π r’2 + π r’’2
= π (20 + 10) × 15.620 + π (10)2 + π (6)2
= 678.85 cm2