Question

Find the amount of water displaced by a solid spherical ball of diameter 2.8cm?

Answer 1

Hint: Here in the given question we know that to calculate the water displaced by an object here we need to calculate the volume of the given shape, because the object will displace the amount of water equal to its volume. Here the given shape is sphere and the diameter is also given so we can solve accordingly.
Formulae Used: Volume of sphere with radius “r” is given by:
\[ \text{Volume of sphere} = \dfrac{4}{3}\pi {r^3}\]

Complete step by step answer:
 Here in the given question we need to find the water displaced by a solid sphere, here we know that a solid object displaces water equal to its volume, so here in order to calculate the water displaced we need to find the volume of sphere, on solving we get:
\[ \Rightarrow Radius = \dfrac{{diameter}}{2} = \dfrac{{2.8}}{2} = 1.4cm\]
Now using the formulae for volume of sphere we get;
\[ \Rightarrow Volume = \dfrac{4}{3}\pi {(1.4)^3} = \dfrac{4}{3} \times 3.414 \times 2.744 = \dfrac{{37.47}}{3} = 12.49c{m^3}\]
Here we get the volume of water displaced by the sphere.

Note: Here in such a type of question, we need to find the volume because when it comes to see that how much space is occupied by any shape, then it comes to volume, that is we need to find the volume for the particular shape in order to get the solution for the question.