Question

Suppose you have a lead ball of mass \[454\,gm\]. What is the ball’s volume? Density of lead (solid) = \[11.35\,gm\,c{{m}^{-3}}\]
(A). \[40\,c{{m}^{3}}\]
(B). \[30\,c{{m}^{3}}\]
(C). \[50\,c{{m}^{3}}\]
(D). \[20\,c{{m}^{3}}\]

Answer 1

Hint: Density is an important physical quantity. It is related to the mass and volume of a body. Substituting the corresponding values in the equation depicting the relation of density, mass, and volume we can calculate the volume. Convert units between different metric systems, if required.
Formulas Used:
\[d=\dfrac{m}{V}\]

Complete step-by-step solution
Mass is the quantity of matter that makes up a body. Its SI unit is \[kg\]
Volume is the 3-dimensional space occupied by a body. Its SI unit is \[{{m}^{3}}\].
Density is the mass per unit volume of a material. Its SI unit is \[kg\,{{m}^{-3}}\]. Its CGS unit is \[gm\,c{{m}^{-3}}\]. It is given as-
\[d=\dfrac{m}{V}\] ----------- (1)
Here, \[d\]is the density of a material
\[m\]is its mass
\[V\]is the volume
Density is one of the most important physical quantities. It is widely used to identify pure substances and to determine the composition of certain bodies. It also helps us to determine which materials can float on water and which cannot. The density of water is \[0.99\,gm\,c{{m}^{-3}}\].
Given for a lead ball, \[m=454\,gm\] and \[d=11.35\,gm\,c{{m}^{-3}}\], substituting in eq (1), we get,
\[\begin{align}
  & 11.35=\dfrac{454}{V} \\
 & \Rightarrow V=\dfrac{454}{11.35} \\
 & \therefore V=40\,c{{m}^{-3}} \\
\end{align}\]
The volume of lead ball is \[40\,c{{m}^{-3}}\]. Therefore, the correct option is (A).

Note: The SI system is the most widely accepted system of units around the world, while the CGS system of units is also a type of metric system wherein the accepted units are- centimeter for length, gram for mass, and second for time. The SI system is greater than the CGS system. Relation between units of density in SI and CGS system is \[1\,kg\,{{m}^{3}}={{10}^{-3}}gm\,c{{m}^{-3}}\]. \[1\,c{{m}^{-3}}\] is equal to \[1\,ml\].