Question

Cylinder A has a diameter of $14$ cm and height of $7$ cm and diameter of cylinder B is $7$ cm and height of $14$ cm. Which cylinder has more volumes, discuss without calculations. Clarify your answer with calculation.

• A. Cylinder $A$ has more volume.
  
• B. Cylinder $B$ has more volume.
• C. Both have same volumes.
  
• D. None of these.
  

Answer 1

The correct option is A Cylinder $A$ has more volume.

We are given,

Cylinder $A$ ahs a diameter of $14cm$

and height of $7cm$

i.e., $d_A=14cm$ & $h_A=7cm$

now, radius $r_A=\frac{d_A}{2}=7cm$

And Cylinder $B$ has a diameter of $7cm$ and height of $14sm$

i.e, $d_B=7cm$ & $h_B=14cm$

now, radius $r_B=\frac{r_B}{2}=3.5cm$

Now, We know that volume of Cylinder is given by, Volume $V=\pi r^{2}h$

$\therefore V\alpha r^2$ & $V\alpha h$

$\therefore V\alpha r^{2}h$

here $r_A>r_B\Rightarrow r_A^2>>r_B^2$

& $h_A<h_B$

$\therefore r_A^2{h}_A>r_B^2{h}_B$

$\therefore \left(VolumeA\right)>\left(Volume\right)B$

$\to$ So, Cylinder $A$ had more Volume

Now, $\left(Volume\right)A=\pi r_A^2{h}_A=\frac{\left(22\right)}{7}\times (7{)}^2\times (7)$

$(Volume{)}_A=1078c{m}^3$

Now, $(Volume{)}_B=\pi r{B}^2{h}_B=\left(\frac{22}{7}\right)\times (3.5{)}^2\times \left(14\right)$

$(Volume{)}_B=539c{m}^3$

So, $(Volume{)}_A>(Volume{)}_B$