Question

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.

A B

Answer 1

STEP 1 : Given

Dimensions of cylinder A

Diameter $=7cm$

Radius $=\frac{7}{2}cm$

Height $=14cm$

Dimensions of cylinder B

Diameter $=14cm$

Radius $=\frac{14}{2}=7cm$

Height $=7cm$

STEP 2 : Suggesting the volume of cylinders without actual calculations

Since the volume of a cylinder is equal to ${\mathrm{\pi r}}^2\mathrm{h}$.

So the volume of a cylinder whose radius is greater should be greater.

Therefore, volume of cylinder B should be greater than cylinder A.

STEP 3 : Finding the volume and surface area of cylinder A

Volume of cylinder A $={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times 14$

Volume of cylinder A $=11\times 7\times 7=539c{m}^3$

Total Surface Area of cylinder A $=2\mathrm{\pi r}\times (h+r)=2\times \frac{22}{7}\times \frac{7}{2}\times \left(14+\frac{7}{2}\right)$

Total Surface Area of cylinder A $=22\times \frac{35}{2}=11\times 35=385c{m}^2$

STEP 4 : Finding the volume and surface area of cylinder B

Volume of cylinder B $={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times 7\times 7\times 7$

Volume of cylinder B $=22\times 49=1078c{m}^3$

Total Surface Area of cylinder B $=2\mathrm{\pi r}\times (h+r)=2\times \frac{22}{7}\times 7\times \left(7+7\right)$

Total Surface Area of cylinder B $=44\times 14=616c{m}^2$

Hence, we can clearly say that volume of cylinder B is greater than volume of cylinder A and also surface area of cylinder B is greater than surface area of cylinder A.