Question

a rectangle sheet of dimesions 22×6 cm is rolled about is shorter side find find valume of solid thus generated​

Answer 1

Volume of Cylinder generated by Rolling a rectangular sheet

Answer: Volume of solid generated that is cylinder is 231 cubic centimeter.

Explanation:

Given that

Dimension of rectangular sheet = 22 x 6 cm

On Rolling rectangular sheet we will get a cylinder.

As sheet is rolled about its shorter side , means shorter side becomes the height of a cylinder generated and longer side becomes circumference of base of cylinder.

So we need to determine the volume of cylinder whoes height = 6 cm and Circumference of the base = 22 cm

as Circumference = 2 π r  where r is radius of the base

=> 2 π r  = 22 cm

=>  2 x (22/7) x r = 22 cm

=>  44r/7 = 22

=> r = (22 x 7) / 44 = 7/2 cm

Now we have radius of base of cylinder r = (7/2) and height if cylinder = 6 cm

Volume of cylinder = $\pi r^{2} h$ = (22/7) x ( 7/2) x (7/2 ) x 6

                                            = 6468/28

                                            = 231 cubic centimeter

Hence Volume of solid generated that is cylinder is 231 cubic centimeter.

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