Question

a right circular cylindrical container of base radius 6 cm and height 15 cm is full of ice cream. the ice cream to be filled in cones of height 9 cm and base radius 3 cm, having a hemispherical cap. find the number of cones needed to empty the container​

Answer 1

Step-by-step explanation: Volume of Ice cream in the container = πr²h = 22/7 * (6)²(15) = 1697.14 cm³. Thus number of cones required = 1697.14/141.43 = 12 cones.

Answer 2

$\sf \Large Solution!!$

$\sf \large Given,$

$\sf \to Base\;radius=6cm$

$\sf \to Height=15cm$

$\sf \to Height\;of\;cone=9cm$

$\sf \to Base\;radius\;of\;cone=3cm$

$\sf \large So,$

$\sf \to Volume\;of\;ice\;cream\;in\;container=\pi r^{2}h$

$\sf \to Volume\;of\;ice\;cream\;in\;container=\frac{22}{7}\times (6)^{2}\times (15)$

$\sf \to Volume\;of\;ice\;cream\;in\;container=1697.14cm^{3}$

$\sf \large So,$

$\sf \to Volume\;of\;ice\;cream\;cone=\frac{2}{3}\pi r^{3}+\frac{1}{3}\pi r^{2}h$

$\sf \to Volume\;of\;ice\;cream\;cone=\frac{2}{3}\times \frac{22}{7}\times (3)^{3}+\frac{1}{3}\times \frac{22}{7}\times (3)^{2}\times 9$

$\sf \to Volume\;of\;ice\;cream\;cone=5\times 9\times \frac{22}{7}$

$\sf \to Volume\;of\;ice\;cream\;cone=141.43cm^{3}$

$\sf \large Hence,$

$\sf \to Number\;of\;cones\;required=\frac{1697.14}{141.43}$

$\sf \to Number\;of\;cones\;required=11.99$

$\sf \boxed{\bigstar Approximately,\;12\;cones\;are\;required!!}$