Question

Ice Cream is to be filed into a cone of height 12 cm and diameter 6cm having the hemispherical space on the top in the volume of ice cream that can be filed into it.
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Answer 1

Answer:

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Explanation:

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Answer 2

height $\rm (h_{1})$ of cylindrical container = 15cm

$\rm Radius= \frac{Diameter}{2}$

$Radius \rm (r_{1})$of circular end of container = 12/2 = 6cm

$Radius \rm (r_{2})$ of circular end of ice cream cone = 6/2 = 3cm

$Height \rm (h_{2})$ of conical part of ice- cream cone = 12cm

Let ice-cream cones be filled with Ice-cream of the container.

volume of Ice-cream in cylinder = n (volume of 1 Ice-cream cone + volume of Hemi spherical shape on the top)

$\begin{gathered}\rm\implies\pi {r}^{2} h = h( \frac{1}{3} \pi {r}^{2} 3h2 + \frac{2}{3} \pi {r}^{3} 2) \\ \end{gathered}$

$\begin{gathered}\rm\implies\pi \times {6}^{2} \times 15 = n( \frac{1}{3} \pi {3}^{2} \times 12 + \frac{2}{3} \pi {3}^{3} ) \\ \end{gathered}$

$\begin{gathered}\rm\implies n = \frac{30 \times 15}{ \frac{1}{3} \times 9 \times 12 + \frac{2}{3} \times 27} \\ \end{gathered}$

$\begin{gathered}\rm\implies n = \frac{36 \times 15 \times 3}{108 + 54} \\ \end{gathered}$

$\begin{gathered}\rm\implies n = 10 \\ \end{gathered}$

So, 10 Ice-cream cones can be filled with Ice-cream in the Container.