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Volume and Surface area of Solids — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsVolume and Surface area of Solids5 Marks
Question
A solid right circular cone of height $60\ cm$ and radius $30\ cm$ is dropped in a right circular cylinder full of water, of height $180\ cm$ and radius 60cm. Find the volume of water left in the cylinder, in cubic metres.
✓

Answer

We have,
Height of cone, $h = 60\ cm,$
The base radius of cone, $r = 30\ cm,$
The height of cylinder, $H = 180\ cm$ and
The base radius of the cylinder, $R = 60\ cm$
Now,
Volume of water left in the cylinder = Volume of cylinder - Volume of cone
$=\pi\text{R}^2\text{H}=\frac{1}{3}\pi\text{r}^2\text{h}$
$=\frac{22}{7}\times60\times60\times180=\frac{1}{3}\times\frac{22}{7}\times30\times30\times60$
$=\frac{22}{7}\times30\times30\times60(2\times2\times3-\frac{1}{3})$
$=\frac{22}{7}\times54000(12-\frac{1}{3})$
$=\frac{22}{7}\times54000\times\frac{35}{3}$
$=1980000\text{cm}^3$
$=\frac{1980000}{1000000}\text{m}^3$
$=1.98\text{m}^3$
So, the volume of water left in the cylinder is $1.98 m^3.$

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