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Surface Areas And Volumes — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsSurface Areas And Volumes3 Marks
Question
Rain water, which falls on a flat rectangular surface of length $6\ m$ and breadth $4\ m$ is transferred into a cylindrical vessel of internal radius $20\ cm.$ What will be the height of water in the cylindrical vessel if a rainfall of $1\ cm$ has fallen$?$
✓

Answer

The fallen rains are in the form of a cuboid of height $1\ cm,$ length $6\ m = 600\ cm$ and breadth $4\ m = 400 \ cm$. Therefore, the volume of the fallen rains is
$V = 600 × 400 × 1 = 240000\ cm^3$
The fallen rains are transferred into a cylindrical vessel of internal radius $r_1= 20\ cm.$ Let, the height of the water in the cylindrical vessel is $h_1\ cm.$ Then, the volume of the water in the cylinder is
$\text{V}_1=\pi\text{r}^2_1\text{h}_1=\frac{22}{7}\times(20)^2\times\text{h}_1$
Since, the volume of the water in the cylinder is same as the volume of the rainfalls, we have
$V_1 =V$
$\Rightarrow\frac{22}{7}\times(20)^2\times\text{h}_1=240000$
$\Rightarrow\text{h}_1=\frac{240000\times7}{(20)^2\times22}$
$\Rightarrow190.9$
Therefore, the height of the water in the cylinder is $190.9\ cm$

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