Question

if the radius of a right circular cylinder is increased by 25 percentage then the percentage increase in the curved surface area is

Answer 1

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✺ Answer:

♦️ GiveN:

• Radius of a right circular cylinder increased by 25%.

♦️ To FinD:

• % change in the curved surface area of cylinder.

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✺ Explanation for Answer:

The above question is based upon the applications of menstruation as well as percentage(arithmatic). As the question is asking for new surface area and % change, let's see the formula to be used:

$\large{ \ast{ \boxed{ \sf{ \green{csa \: of \: cylinder = 2\pi rh}}}}}$

$\large{ \ast{ \boxed{ \sf{ \green{\%change = \frac{final - initial}{initial} \times 100}}}}}$

By using these formulae, let's find out the solution of the question.

↪ Refer to the attachment.....

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✺Solution:

Let the original radius be r

% change in radius = 25 %

Then new radius,

$\large{ \sf{ \dashrightarrow \: r_n = r + 25\% \: of \: r}} \\ \\ \large{ \sf{ \dashrightarrow \: r_n = r + \frac{25}{100} \times r}} \\ \\ \large{ \sf{ \dashrightarrow \: r_n = \frac{100r + 25r}{100}}} \\ \\ \large{ \sf{ \dashrightarrow \: r_n = \cancel{\frac{125r}{100}}}} \\ \\ \large{ \sf{ \dashrightarrow \: r_n = \frac{5r}{4} }}$

Initial curved surface area = 2 πrh

So, our new curved surface area = 2 π× 5r/4×h

By using formula,

$\large{ \sf{ \dashrightarrow \: \% \: change \: in \: area = \frac{final \: CSA - initial \: CSA}{initial \: CSA} \times 100}} \\ \\ \large{ \sf{ \dashrightarrow \: final \: CSA- initial \: CSA = 2\pi \times (\frac{5}{4} r)h - 2\pi rh}} \\ \\ \large{ \sf{ \dashrightarrow \: final \: CSA - initial \: CSA= \frac{5 \times 2\pi \times rh - 4 \times 2\pi \times rh}{4}}} \\ \\ \large{ \sf{ \dashrightarrow \: final \: CSA - initial \: CSA= \frac{2\pi \times rh (5-4)}{4}}}\\ \\ \large{ \sf{ \dashrightarrow \: final \: CSA- initial \: CSA = \frac{2\pi rh }{4}}}$

Calculating % change in area,

$\large{ \sf{ \dashrightarrow \: \% \: change \: in \: CSA = \frac{ \frac{2\pi rh}{4} }{2\pi rh} \times 100}} \\ \\ \large{ \sf{ \dashrightarrow \: \% \: change \: in \: CSA = \frac{1}{4} \times 100}} \\ \\ \large{ \sf{ \dashrightarrow \: \% \: change \: in \: CSA = \boxed{ \sf{ \red{25\%}}}}} \\ \\ \large{ \therefore{ \underline{ \sf{ \green{ So \: the \: CSA \: of \: cylinder\: increased \: by \: 25\%}}}}}$

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