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Chapter 7: Problem 1062

If the length of a cylinder on heating increases by \(2 \%\) the area of its base will increase by. (A) \(0.5 \%\) (B) \(2 \%\) (C) \(1 \%\) (D) \(4 \%\)

Short Answer

Expert verified
Since the radius of the cylinder's base remains the same after heating (r'= r), the area of the base also remains the same (A'= A = πr^2). Therefore, there is no increase in the area of the base, which means the correct answer is: (C) 0%

Step by step solution

01

Find the new radius after heating

Since the problem only mentions the increase in length of the cylinder, we can assume that the radius does not change when heated. Therefore, the radius before and after heating will be the same (r).
02

Calculate the area of the base before and after heating

The area of the base before heating is given by the formula A = πr^2. Since the radius remains the same after heating, the area of the base after heating will also have the same formula A' = πr'^2. However, since r' = r, we have A' = πr^2.
03

Compare the two base areas and find the percentage increase

Since the area of the base before and after heating is the same, A = A', there is no increase in the area of the base. The percentage increase in the area of the base would be: (\( \frac{A'-A}{A} \)) * 100% = (\( \frac{πr^2 - πr^2}{πr^2} \)) * 100% = 0% Therefore, the area of the base does not increase after heating. The correct option is: (C) 0%

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