Question

Question 2
The diameter of cylinder A is 7 cm and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area.

Answer 1

Yes, we can say that volume of cylinder B is greater, since radius of cylinder B is greater than that of cylinder A (and square of radius gives more value than previous).
Diameter of cylinder A = 7 cm $\Rightarrow \text{Radius of cylinder A}=\frac{7}{2}cm$
And Height of cylinder A = 14 cm
$\therefore$ Volume of cylinder $A=\pi r^{2}h=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 14=539c{m}^2$
Now, Diameter of cylinder B = 14 cm
$\Rightarrow \text{Radius of cylinder B}=\frac{14}{2}=7cm$
And Height of cylinder B = 7 cm
$\therefore$ Volume of cylinder $A=\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 7=1078c{m}^2$
Total surface of cylinder $A=2\pi r(h+r)\text{[It is open from top]}=2\times \frac{22}{7}\times \frac{7}{2}(14+\frac{7}{2})=385c{m}^2$
Total surface of cylinder $B=2\pi r(h+r)\text{[It is open from top]}=2\times \frac{22}{7}\times 7(7+7)=616c{m}^2$
Yes, cylinder with greater volume also has greater surface area