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Surface Areas and Volumes — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsSurface Areas and Volumes5 Marks
Question
A solid right circular cone of height 120cm and radius 60cm is placed in a right circular cylinder full of water of height 180cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.
✓

Answer



Cone is placed inside the cylindrical vessel full of water.
So, the volume of water from cylinder will over flow equal to the volume of cone.
Hence, the water left in cylinder = Volume of cylinder - Volume of cone (i)
Volume of water left after immersing the cone into cylinder full of water = Volume of cylider - Volume of cone
$=\pi\text{R}^2\text{H}-\frac{1}{3}\pi\text{r}^2\text{h}$
$\therefore$ Required volume of water in cylinder
$=\pi\text{r}^2\text{H}-\frac{1}{3}\pi\text{r}^2\text{h}$ $[\because\text{R}=\text{r}]$
$=\pi\text{r}^2\Big[\text{H}-\frac{1}{3}\text{h}\Big]$ $=\frac{22}{7}\times60\times60\Big[180-\frac{120}{3}\Big]$
$=\frac{22}{7}\times60\times60\times140\text{cm}^3$
$=\frac{22\times60\times60\times140}{7\times100\times100\times100}=\frac{22\times72}{1000}=\frac{1584}{1000}$
$\therefore$ Volume of water in cylinder $= 1.584m^3$​​​​​​​
Hence, required volume of water left $= 1.584m^3.$

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