Question
The given figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volurne of the solid.
✓
Answer
Height of cylinder = 6.5cmheight of cone $= h_2 = (12.8 - 6.5)cm = 6.3cm$
Radius of cylinder = radius of cone
= radius of hemisphere
$=\Big(\frac{7}{2}\Big)\text{cm}$
Volume of solid = volume of cylinder + volume of cone + volume of hemisphere
$=\pi\text{r}^2\text{h}_1+\frac{1}{3}\pi\text{r}^2\text{h}_2+\frac{2}{3}\pi\text{r}^2\Big(\text{h}_1+\frac{1}{3}\text{h}_2+\frac{2}{3}\text{r}\Big)$
$=\Big[\frac{22}{7}\times3.5\times3.5\times\Big(6.5+6.3\times\frac{1}{3}+\frac{2}{3}\times3.5\Big)\Big]$
$=[(38.5)\times(6.5+2.1+2.33)]\text{cm}^3$
$=(38.5\times10.93)\text{cm}^3=420.80\text{cm}^3$
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