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Question

Mathematics Question on Volume and Capacity

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.
Diameter of cylinder

Answer

The heights and diameters of these cylinders A and B are interchanged.
We know that,
Volume of cylinder = πr2h\pi r^2h
If measures of r and h are same, then the cylinder with greater radius will have greater area.
Radius of cylinder A = 72\frac{7}{2} cm

Radius of cylinder B = 142\frac{14}{2} cm = 7 cm
As the radius of cylinder B is greater, therefore, the volume of cylinder B will be greater.
Let us verify it by calculating the volume of both the cylinders.
Volume of cylinder A = πr2h\pi r^2h
=(227)×(72)×(72)×14=539= (\frac{22}{7} )×(\frac{7}{2})×(\frac{7}{2})×14 = 539 cm3
Volume of cylinder B = πr2h\pi r^2h
=(227)×7×7×7=1078= (\frac{22}{7})×7×7×7 = 1078 cm3

Volume of cylinder B is greater.
Surface area of cylinder A = 2πr(r+h) 2\pi r(r+h )
=2×227×72×(72+14)=385= 2 \times \frac{22}{7} \times \frac{7}{2} \times (\frac{7}{2} + 14) = 385
Surface area of cylinder A is 385 cm2

Surface area of cylinder B =2πr(r+h)=2\pi r(r+h )
=2×(227)×7(7+7)=616= 2×(\frac{22}{7})×7(7+7) = 616
Surface area of cylinder B is 616 cm2
Thus, the surface area of cylinder B is also greater than the surface area of cylinder A.