Question

a container having shape of a right circular cylinder with 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 calculate the number of such cones which can be filled with ice cream​

Answer 1

Answer:

HoPE IT HELPS YOU BUDDY... FOLLOW ME FOR MORE ANSWERS AND HELP.. ALL THE BEST

Answer 2

$\huge\underline\textsf{Explantion:- }$

$\footnotesize{\boxed{\sf Number \: of \: cone = \dfrac{Volume \: of \: cylinder}{Volume \: of \: ice \: cream}}}$

$\large\underline\textsf{Volume of cylinder }$

$\implies\sf Diameter = 12cm$

$\implies\sf Radius = \dfrac{Diameter}{2} = 6cm$

$\large\underline{\boxed{\sf Volume \:of\: cylinder = \pi r^2h}}$

$\implies\pi(6) {}^{2} \times( 15)$

$\implies\sf\pi(6 \times 6) \times (15)$

$\implies\sf\red{540\pi}$

$\small\underline\textsf{Volume of ice cream cone}$

$\footnotesize{\boxed{\sf Volume \: of \: ice \: cream\: cone + volume \: of \: hemishphere}}$

$\large\underline\textsf{Volume of cone }$

$\implies\sf Diameter = 6$

$\implies\sf Radius = \dfrac{Diameter}{2} = 3cm$

$\implies\sf Height = 12cm$

$\implies\sf Volume \: of \: cone \: = \dfrac{1}{3} \pi \: r {}^{2} h$

$\boxed{\sf \dfrac{1}{3} \times \pi \times (3) {}^{2} \times (12)}$

$\implies\sf\red{36\pi}$

$\large\underline\textsf{ Volume of hemisphere }$

$\sf Radius = \dfrac{Diameter}{2} = 3cm$

$\implies\sf Volume \: of \: hemisphere = \dfrac{2}{3} \pi \: r {}^{3}$

$\implies\sf \dfrac{2}{3} \times \pi \times (3) {}^{3} = \red{18\pi}$

$\small\underline\textsf{Hence, }$

$\large\underline\textsf{Volume of ice-cream }$

$\sf Volume \: of \: cone + volume \: of \: hemisphere$

$\implies\sf36\pi + 18\pi$

$\small\underline\textsf{Now, }$

$\footnotesize{\boxed{\sf Number \: of \: cone = \dfrac{Volume \: of \: cylinder}{Volume \: of \: ice \: cream \: cone}}}$

$\implies\sf \dfrac{540\pi}{54\pi}$

$\sf So ,\: the \: number \: ofcone = 10$