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.

Answer 1

Answer:

10

Step-by-step explanation:

Given, Diameter = 12 cm.

Then, radius = 6 cm.

Volume of cylinder = πr²h

                               = π(6)² * 15

                               = 540π cm³.

Volume of cone having hemispherical shape on the top:

Given, height = 12 cm and radius = d/2 = 3 cm.

= (1/3) πr²h + (2/3) πr³

= (1/3)πr²[h + 2r]

= (1/3)π(3)²[12 + 6]

= (1/3) * 9π[18]

= 54π cm³

Number of such cones = 540π/54π

                                      = 10.

Hope it helps!

Answer 2

$\huge\underline\mathrm\orange{SOLUTION:-}$

$\footnotesize{\boxed{\sf number \: of \: cone = \frac{volume \: of \: cylinder}{volume \: of \: ice \: cream}}}$

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

$\implies\sf diameter = 12cm$

$\implies\sf radius = \frac{diameter}{2} = 6cm$

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

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

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

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

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

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

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

$\implies\sf diameter = 6$

$\implies\sf radius = \frac{diameter}{2} = 3cm$

$\implies\sf hieght = 12cm$

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

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

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

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

$\sf radius = \frac{diameter}{2} = 3cm$

$\implies\sf volume \: of \: hemisphere = \frac{2}{3} \pi \: r {}^{3}$

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

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

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

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

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

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

$\footnotesize{\boxed{\sf number \: of \: cone = \frac{volume \: of \: cylinder}{volume \: of \: ice \: cream \: cone}}}$

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

$\sf {So ,\: the \: number \: of \: cone = 10}$