Question

Find the height of the cylinder whose volume is $1.54{m^3}$ and the diameter of base is $140cm$ ?
A.$1{\text{ }}m$
B.$1.1{\text{ }}m$
C.$5{\text{ }}m$
D.None of these

Answer 1

Here before solving this question we need to know the following formula: -
Volume of cylinder $= \pi {r^2}h\,\,\,\,\,\,\,\,\,\,...(1)$
Where,
$r =$radius of the base of the cylinder and
$r = \dfrac{{{\text{Diameter}}}}{2}$
$h =$height of the cylinder
According to this question we have,

Complete step by step solution:
$r = \dfrac{{140}}{2} \\\ r = 70cm \\\ r = 0.7m \\\$
And
Volume$= 1.54{m^3}$
Let the height of the cylinder is $h$ meter.
Substitute all the values in the equation $\left( 1 \right)$ .
$1.54 = \pi {(0.7)^2}h \\\ 1.54 = 0.49\pi h \\\ h = \dfrac{{1.54}}{{0.49\pi }} \\\$
Using, $\pi = \dfrac{{22}}{7}$ then,
$h = \dfrac{{1.54 \times 7}}{{0.49 \times 22}} \\\ h = 1 \\\$
Thus, the height of the cylinder is $1$ meter.
Hence, the correct option is $A$ .

Note: Here there are the chances of calculation mistakes and we need to focus on the calculation part. Moreover while applying formula we must write all the values first and choose the formula according to the need to question.