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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.
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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 = 120cm
Radius of a right circular cone = 60cm
$\therefore$ 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 = 1440007cm3 [from point (i)]
Given that, height of a right circular cylinder = 180cm
and radius of a right circular cylinder = Radius of a right circular cone = 60cm

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