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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 - CBSE Class 8 - Mathematics

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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?

Solution

The heights and diameters of these cylinders A and B are interchanged.

We know that,

Volume of cylinder = `pir^2h`

If measures of r and h are same, then the cylinder with greater radius will have greater area

Radius of cylinder A = `7/2` cm

Radius of cylinder B = `(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 = `pir^2h`

= `(22/7 xx 7/2 xx 7/2 xx 14) cm^3`

= 539 cm3

Volume of cylinder B = `pir^2h`

= `(22/7 xx 7 xx 7 xx 7) cm^3`

= 1078 cm3

Volume of cylinder B is greater.

Surface area of cylinder A = `2pir (r  + h)`

= `[2 xx 22/7 xx 7/2 (7/2 + 14)] cm^2`

= `[22 xx ((7+28)/2)] cm^2`

= `(22 xx 35/2) cm^2`

= `385 cm^2`

Surface area of cylinder B  = `2pir (r + h)`

= `[2 xx22/7 xx 7 xx (7 + 7)] cm^2`

= (44 x 14) cm2

= 616 cm2

Thus, the surface area of cylinder B is also greater than the surface area of cylinder A.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 8 (2018 to Current)
Chapter 11: Mensuration
Ex. 11.40 | Q: 2 | Page no. 191
Solution 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 Concept: Volume of Cube, Cuboid and Cylinder - Conept of Cylinder.
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