Question

A solid cylinder has a radius of 2cm and a length of 7cm. It has a density of \[3.1g/c{m^3}\] . What is the mass of the cylinder?

Answer 1

Hint: we have to find the mass of the cylinder since density is given in the problem so we can use the relation between mass and density to find the mass of a cylinder further we need volume of a cylinder so we can use the formula to find the volume of a cylinder and is given by \[v = \pi {r^2}h\].

Complete step by step answer:
First let us list the given data in the problem
Given:
Radius of solid cylinder (\[r\])\[ = 2cm\]
Length of solid cylinder (\[h\])\[ = 7cm\]
Density of solid cylinder (\[\rho \])\[ = 3.1g/c{m^3}\]
Mass (\[m\])\[ = ?\]
Now let us consider the relation between mass and density and is given by \[\rho = \dfrac{m}{v}\]
Where \[m\]is the mass of a cylinder and \[v\] is the volume of a cylinder.
Since the value of density is given in the problem but volume is not given so we calculate it by using the formula \[v = \pi {r^2}h\]
Since the values of r and h is given now substituting it in the above formula we get
\[v = \dfrac{{22}}{7} \times {2^2} \times 7\]
\[ \Rightarrow v = (3.14) \times 4 \times 7\]
On simplification we get
\[ \Rightarrow v = 87.92c{m^3}\]
Now substitute \[v\]and \[\rho \]in equation 1 we get
\[3.1 = \dfrac{m}{{87.92}}\]
Cross multiply we get
\[m = 272.552grms\]
Hence the mass of the cylinder is \[m = 272.552grms\].

Note: Since in the given problem the unit for density is given as \[g/c{m^3}\]meaning is unit of mass is grams whereas the unit of the volume is in terms of \[c{m^3}\]therefore the unit of mass is given as grams in obtained answer. If the unit of density is given in terms of \[kg/c{m^3}\]then the unit of mass will be kg.