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Let's do this question, a rectangular sheet of dimensions, twenty five centimeters into seven centimeters

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is rotated about its longer side.

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Find the volume and the whole surface area of the solid that's generated.

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All right.

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What's the video?

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Give it a try and then let's do it together.

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All right.

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We're back.

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Let's do it together.

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Now, if you take a rectangular sheet of paper, right, and you rotated about, it's longer same.

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So let this be the longer side.

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But what does rotating it about the longest side mean, you keep turning it like this, right?

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So this will turn out to become a cylinder.

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Right, so you get a cylinder when you rotate a rectangular sheet, all right.

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Now, what would be the dimensions of the cylinder?

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The dimensions would be twenty five centimeters would be the height.

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Right.

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Because that's this height over here.

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And we have rotated it about its longer side.

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Right.

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That's why you can see from the figure this will be twenty five centimeter and this part.

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Right.

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This is this was the initial sheet that we had.

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And we know this is equal to seven centimeter and that is the radius of this base over here.

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Right.

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Therefore, the radius is seven centimeter and the height will be twenty five centimeters.

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Now we need to find the volume and the whole surface area of the solid.

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Right.

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So volume is biased coverage for a cylinder that's equal to twenty two by seven inch to seven square

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inch to twenty five.

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And this simplifies two three eight five zero centimetre cube.

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All right.

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Now what about the surface area.

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That's two Pyar Square because you have two bases plus two Pyaar.

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It's right to surface area.

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Total surface area is to Pyaar squared plus two by our edge.

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Let's substitute values.

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That's two hundred twenty two by seven to seven squared plus two in twenty two by seven into seven into

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twenty five.

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And that simplifies two one four zero eight centimeter square.

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That is your answer.