Question

cylinder having height and base diameter 2m and a cube having sides 2m are filled with the same

liquid. In which case, liquid will be exerting more pressure at the bottom?​

Answer 1

GiveN :-

• A cylinder has a height and base diameter 2m.
• A cube has sides of 2 m .
• They are filled with same liquid.

To FinD :-

• In which case, liquid will be exerting more pressure at the bottom .

SolutioN :-

We know that Pressure is inversely proportional to Area which means on increasing the area the pressure will decrease and on decreasing area the pressure will increase . That is ,

$\sf:\implies \gray{ Pressure \propto \dfrac{1}{Area} }$ .

So here let's find out the area of base in both cases . The case in which the base area will be less will experience more force .

Case 1: Finding the area of Cylinder :-

$\sf:\implies \pink{ Base \ Area_{(cylinder)}= \pi r^2 }\\\\\sf:\implies Base \ Area_{(cylinder)}= \pi \times \left(\dfrac{2m}{2}\right)^2 \\\\\sf:\implies Base \ Area_{(cylinder)}= \dfrac{22}{7}(1) m^2 \\\\\sf:\implies \boxed{\pink{\frak{ Base \ Area_{(cylinder)}= 3.14 \ m^2 }}}$

$\rule{200}2$

Case 2: Finding the area of Cube :-

$\sf:\implies\pink{ Base \ Area_{(Cube)} = a^2} \\\\\sf:\implies Base \ Area_{(Cube)} = (2m)^2 \\\\\sf:\implies \boxed{\pink{\frak{ Base \ Area_{(Cube)} = 4m^2 }}}$

Hence here we see that the area of base of cube is more than the area of base of the cylinder . So the cylinder's base will exert more pressure on the ground .

$\boxed{\boxed{\textsf{ \gray{Hence the \red{cylinder} will experience more pressure on the ground .}}}}$