Question

Find the height (h) of the cylinder where volume (v) is $154 m^3$ and the diameter of the base is 140cm?

Answer 1

Hint: Here the given question is to find the height of the cylinder in which we are given with the volume and the base of the cylinder, here we need to use the formulae for the volume of the cylinder in which we know that the volume of the cylinder is the area of the base of the cylinder multiplying the height of the cylinder.

Formula used: Volume of a cylinder is given by:
\[ \Rightarrow volume = \pi \times {\left( {\dfrac{d}{2}} \right)^2} \times h\]

Complete step by step solution:
Here the given question asked the height of the cylinder and the volume along with the length of the base of the cylinder is provided to us, on solving this question we have to use the formulae of the volume of the cylinder, here we need to first write the formulae then put the associated values, and then on doing mathematical operation we will get the solution for the question. On solving we get:
\[ \Rightarrow volume = \pi \times {\left( {\dfrac{d}{2}} \right)^2} \times h\]
Here:
V=volume of cylinder=154 m3
d=base length=140cm=1.4m (since 100cm=1m)
h=height of cylinder
On putting values and solving the question we get:
\[
   \Rightarrow volume = \pi \times {\left( {\dfrac{d}{2}} \right)^2} \times h \\
   \Rightarrow 154 = \pi \times {\left( {\dfrac{{1.4}}{2}} \right)^2} \times h \\
   \Rightarrow 154 = 3.14 \times {(0.7)^2} \times h \\
   \Rightarrow h = \dfrac{{154}}{{3.14 \times 0.49}} = \dfrac{{154}}{{1.5386}} = 100.09 \\
 \]
Hence the height of the cylinder is 100.09 m.

Note: Here for the statement question in which we rae asked for a quantity of any figure in which rest of the quantities are given, here we need to use the direct formulae of for the given quantity and then after putting the values given we can solve for the quantity which is needed to be obtained.