There is a rectangular metal plate in which two cavities in the shape of a rectangle and a circle are made, as show with dimensions. $P$ and $Q$ are centers of these cavities. On heating the plate, which of the following quantities increase?

π r^{2}

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$a b$

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$R$

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$b$

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Solution

The correct option is D
$b$

As a body expands due to a rise in temperature, all its internal dimensions must increase too. Quite like the letters "HAPPY BIRTHDAY” on a birthday balloon, as one blows it larger. In the figure, as the metal plate expands, so will all the cavities. Due to the overall expansion, the two cavities will move away from each other. Hence, all the attributes - $a$ , $b$ , $a b$ , $R$ and $r$ (and hence $π r^{2}$ ) must increase on heating.

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There is a rectangular metal plate in which two cavities in the shape of a rectangle and a circle are made, as show with dimensions. P and Q are centers of these cavities. On heating the plate, which of the following quantities increase?

There is a rectangular metal plate in which two cavities in the shape of a rectangle and a circle are made, as show with dimensions. $P$ and $Q$ are centers of these cavities. On heating the plate, which of the following quantities increase?