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Question

The following figure represents a solid consisting of a right circular cylinder with a hemisphere at one end and a cone at the other. Their common radius is $$7$$cm. The height of the cylinder and cone are each of $$4$$cm. Find the volume of the solid.
793985_8b1f7be85d3a4f09a773be866f0a41c4.png


Solution

The solid can be divided into $$3$$ parts.

The first part is the cone with height $$4\;cm$$ and radius $$7\;cm$$.

Volume of cone 
 $$\displaystyle V_1=\dfrac{1}{3}\pi r^2 h\\ = \dfrac{1}{3}\cdot \dfrac{22}{7}\cdot 7^2 \cdot 4\\= 205.34\; cm^3$$

The second part is the cylinder with height $$4\;cm$$ and radius $$7\;cm$$.
Volume of cylinder
 $$\displaystyle  V_2=\pi r^2 h\\=\dfrac{22}{7} \cdot 7^2 \cdot 4 \\= 616\; cm^3$$

The third part is the hemisphere with radius $$7\;cm$$.
Volume of hemisphere 
 $$\displaystyle  V_3=\dfrac{2}{3}\pi r^3\\ =  \dfrac{2}{3}\cdot \dfrac{22}{7}\cdot 7^3\\= 718.67\;cm^3$$

Volume of total solid 
$$V_1+V_2+V_3=1540\; cm^3$$

Mathematics

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