Saved Bookmarks
| 1. |
A right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream. |
|
Answer» Given radius of cylinder (r’) = \(\frac{12}2\) = 6 cm Given radius of hemisphere (r’’) = \(\frac{6}2\) = 3 cm Given height of cylinder (h) = 15 cm Height of cone (l) = 12 cm Volume of cylinder = πr2h = πr(6)2(15) cm ………. (1) Volume of each cone = Volume of cone + Volume of hemisphere V = π(r)2(l) + \(\frac{2}3\) π(r)3 V = π(3)2(12) + \(\frac{2}3\) π(3)3 ………… (2) Let number of cone be n n (volume of each cone) = volume of cylinder n = [( \(\frac{1}3\) π(3)2 (12) + \(\frac{2}3\) π(3)3] = π(16)2 15 ⇒ n = 10 |
|