Question

a right circular cylinder having diameter 12 cm and height 15 cm is full of 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 then the number of such cones can be filled with ice cream is? ​

Answer 1

Refer the attachment ..

Answer 2

Answer:

$\large{\underline{\boxed{\sf \:n \:= \:10}}}$

Step-by-step explanation:

$\large \:Diameter \:of \:cylinder \:= \:12 \:cm$

$\large \:Radius \:= \frac{12}{2} \:= \:6 \:cm$

$\large \:Height \:= \:15 \:cm$

$\large \:Volume \:of \:cylinder \:= \:πr^{2}h$

$\large \:= \frac{22}{7} \:× \:6 \:× \:6 \:× \:15$

$\large \:= \frac{11880}{7} cm^{3}$

$\large \:Diameter \:of \:cone \:= \:6 \:cm$

$\large \:Radius \:= \frac{6}{2} \:= \:3 \:cm$

$\large \:Height \:= \:12 \:cm$

$\large \:Volume \:of \:cone \:of \:full \:ice \:cream$

$\large \:Volume \:of \:cone \:+ \:Volume \:of \:hemisphere.$

$\large \:= \frac{1}{3} π \:( \:r^{2}h \:+ \:2r^{3} \:)$

$\large \:= \frac{1}{3} \:× \frac{22}{7} \:( \:9 \:× \:12 \:+ \:2 \:× \:27 \:)$

$\large \:= \frac{1}{3} \:× \frac{22}{7} \:( \:162 \:)$

$\large \:= \frac{22}{21} \:× \:162 \:= \frac{22}{7} \:× \:54$

$\large \:= \frac{1188}{7}$

$\large \:Number \:of \:cones \:required \:to \:fill \:the \:ice \:cream \:= \:n$

$\large \:n \:× \:Volume \:of \:cone \:full \:with \:ice \:cream$

$\large \:= \:Volume \:of \:cylindrical \:ice \:cream \:container$

$\large \:n \:× \frac{1188}{7} \:= \frac{1188}{7}$

$\large \:n \:= \frac{11880}{1188}$

$\large \:n \:= \:10$