Question

$\large \pink\red \pink{\bf{Solution}}$
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into 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 1

$\dashrightarrow \huge \sf \blue{question}$

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into 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.

$\sf \huge\green{answer} \downarrow$

Number of cone is 10.

$\huge\dag\sf\red{explaination}$

Number of cones=

$\sf\frac{volume \: of \: cylinder}{volume \: of \: cone}$

Volume of cylinder

Diameter =12cm

Radius=

$\sf \red{ \frac{diameter}{2}} \\ \\ = \frac{ { \cancel{12}} \: \: ^{6} }{ \cancel2} \\ \\ = 6cm$

Height=15cm

Volume of cylinder=

$\pi r ^{2}h \\ \\ = \pi {(6)}^{2} \times 15 \\ \\ = \pi(6 \times 6) \times 15 \\ \\ \\ 540\pi$

Volume of ice cream cone

=volume of cone+its hemisphere

Diameter=6

Radius=

$\frac{ { \cancel6} \: \: ^{3} }{ \cancel2} \\ \\ = 3cm$

Height=12cm

Volume of cone

$= \frac{1}{2} {\pi r}^{2}h \\ \\ = \frac{1}{3} \times \pi \times {(3)}^{2} \times 12 \\ \\ = 36\pi$

Volume of hemisphere

$= 2\pi r ^{3} \\ \\ = \frac{2}{3} \times \pi \times {(3)}^{3} \\ \\ = 18\pi$

Volume of ice cream cone

$= 36\pi + 18\pi \\ \\ = 54\pi$

Now number of cones

$= \frac{ { \cancel{540} \: \: }^{10} }{ \cancel{54}} \\ \\ \boxed { \sf \blue{10 \: cones}}$

$\Large\textsf{Hope \: It \: Helped}$