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Surface Areas And Volumes — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsSurface Areas And Volumes4 Marks
Question
A solid right circular cone of height $120\ cm$ and radius $60\ cm$ is placed in a right circular cylinder full of water of height $180\ cm$ 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

  1. Whenever we placed a solid right circular cone in a right circular cylinder with full of water, then volume of a solid right circular cone is equal to the volume of water failed from the cylinder.
  2. Total volume of water in a cylinder is equal to the volume of the cylinder.
  3. Volume of water left in the cylinder = Volume of the right circular cylinder – Volume of a right circular cone.

Now, given that
Height of a right circular cone $= 120\ cm$
Radius of a right circular cone $= 60\ cm$
$\therefore$ Volume of a right circular cone $=\Big(\frac{1}{3}\Big)\pi\text{r}^2\times\text{h}$
$=\Big(\frac{1}{3}\Big)\times\Big(\frac{22}{7}\Big)\times60\times60\times120$
$=\Big(\frac{22}{7}\Big)\times20\times60\times120$
$=144000\pi\text{cm}^3$
$\therefore$ Volume of a right circular cone = Volume of water failed from the cylinder $= 1440007\ cm3$ [from point $(i)]$
Given that, height of a right circular cylinder $= 180\ cm$
and radius of a right circular cylinder = Radius of a right circular cone $= 60\ cm$

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