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  • A right cylindrical container of radius 6 cm and height 15 cm is full of ice-cream, which has to be distributed to 10 children in equal cones having hemispherical shape on the top. If the height of the conical portion is four times its base radius, fin

A right cylindrical container of radius 6 cm and height 15 cm is full of ice-cream, which has to be distributed to 10 children in equal cones having hemispherical shape on the top. If the height of the conical portion is four times its base radius, find the radius of the ice-cream cone.

 

 

Answers (1)

radius of cylindrical container = 15 cm

Height of cylindrical container = 6 cm

\begin{align*}\text{Volume of cylinder} & = \pi r^2 h \quad = \text{Volume of ice-cream in the cylindrical containder} \\ & = \pi\times 6^2 \times 15 \\ & = 36\times 15\pi \end{align*}

\begin{align*}\text{Volume of each cone with hemispherical top} & = \frac{1}{3}\pi R^2 H + \frac{2}{3}\pi R^3 \\ & =\frac{1}{3}\pi R^2 (H + 2R) \\ & = \frac{1}{3}\pi x^2 (4x + 2x) \qquad \left\{\text{Let Radius} = x\right \} \\& = 2\pi x^3\end{align*}

Now, the volume of ice-cream in container = 10 \times \text{Volume of each cone}

            \begin{align*} \Rightarrow 36\times 15\pi & = 10\times 2\pi x^3 \\ \Rightarrow x^3 & = \frac{36\times 15}{20} = 27 \\ \Rightarrow x & = 3 cm \end{align*}

Ans- Radius of the ice-cream cone is 3 cm,

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Safeer PP

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