Question

$\large\pink{\bf{question}}$
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

Given :

• Diameter of Cylinder = 12 cm
• Height of Cylinder = 15 cm
• Height of Cone = 12 cm
• Diameter of Cone = 6 cm

To Find :

• No. of Ice Cream = ?

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SolutioN :

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Volume{\small_{(Cylinder)}} = \pi {r}^{2} h }}}}}$

• ${\underline{\boxed{\pmb{\sf{ Volume{\small_{(Cone)}} = \dfrac{1}{3} \pi {r}^{2} h }}}}}$

• ${\underline{\boxed{\pmb{\sf{ Volume{\small_{(HemiSphere)}} = \dfrac{2}{3} \pi {r}^{3} }}}}}$

Where :

• $\sf{ \pi = \dfrac{22}{7} }$

• r = Radius
• h = Height

$\maltese$ Calculating the No. of Ice Creams :

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ Volume{\small_{(Cylinder)}} }{ Volume{\small_{(Cone)}} + Volume{\small_{(Hemisphere)}} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \pi {r}^{2} h }{ \dfrac{1}{3} \pi {r}^{2} h + \dfrac{2}{3} \pi {r}^{3} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \bigg[ \pi \times \bigg( { \dfrac{Diameter}{2} } \bigg)^{2} \times 15 \bigg] }{ \bigg[ \dfrac{1}{3} \times \pi \times \bigg( { \dfrac{Diameter}{2} } \bigg)^{2} \times 12 \bigg] + \bigg[ \dfrac{2}{3} \times \pi \times \bigg( { \dfrac{Diameter}{2} } \bigg)^{3} \bigg] } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \bigg[ \pi \times \bigg( { \dfrac{12}{2} } \bigg)^{2} \times 15 \bigg] }{ \bigg[ \dfrac{1}{3} \times \pi \times \bigg( { \dfrac{6}{2} } \bigg)^{2} \times 12 \bigg] + \bigg[ \dfrac{2}{3} \times \pi \times \bigg( { \dfrac{6}{2} } \bigg)^{3} \bigg] } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \bigg[ \pi \times \bigg( { \cancel\dfrac{12}{2} } \bigg)^{2} \times 15 \bigg] }{ \bigg[ \dfrac{1}{3} \times \pi \times \bigg( { \cancel\dfrac{6}{2} } \bigg)^{2} \times 12 \bigg] + \bigg[ \dfrac{2}{3} \times \pi \times \bigg( { \cancel\dfrac{6}{2} } \bigg)^{3} \bigg] } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \bigg[ \pi \times \bigg( { 6 } \bigg)^{2} \times 15 \bigg] }{ \bigg[ \dfrac{1}{3} \times \pi \times \bigg( { 3 } \bigg)^{2} \times 12 \bigg] + \bigg[ \dfrac{2}{3} \times \pi \times \bigg( { 3 } \bigg)^{3} \bigg] } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \bigg( \pi \times 36 \times 15 \bigg) }{ \bigg( \dfrac{1}{3} \times \pi \times 9 \times 12 \bigg) + \bigg( \dfrac{2}{3} \times \pi \times 27 \bigg) } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \bigg( \pi \times 540 \bigg) }{ \bigg( \dfrac{1}{\cancel3} \times \pi \times \cancel9 \times 12 \bigg) + \bigg( \dfrac{2}{\cancel3} \times \pi \times \cancel{27} \bigg) } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \bigg( \pi \times 540 \bigg) }{ \bigg( 1 \times \pi \times 3 \times 12 \bigg) + \bigg( 2 \times \pi \times 9 \bigg) } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \bigg( \pi \times 540 \bigg) }{ \bigg( \pi \times 36 \bigg) + \bigg( \pi \times 18 \bigg) } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \pi \times 540 }{ \pi \times 36 + \pi \times 18 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \pi \times 540 }{ \pi \times 54 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ \cancel{\pi} \times 540 }{ \cancel{\pi} \times 54 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \dfrac{ 540 }{ 54 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { No. \; of \; Ice \; Cream = \cancel\dfrac{ 540 }{ 54 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\sf{ No. \; of \; Ice \; Cream = 10 }}}}} \; {\purple{\bigstar}} \\ \\ \\ \end{gathered}$

$\therefore \;$ 10 Ice Creams can be filled from the Cylindrical Container .

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Answer 2

Answer:

ʜᴏᴘᴇ ɪᴛs ʜᴇʟᴘ ʏᴏᴜ...

Step-by-step explanation:

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