Area Questions Answers

• 29. If the circumference of a circle increases from 4pi to 8 pi, what change occurs in the area ?

  1. Area is quadrupled
  2. Area is tripled
  3. Area is doubles
  4. Area become half

  Answer And Explanation

  Answer: Option A

  Explanation:

  \begin{aligned}
  2\pi R1 = 4 \pi \\
  => R1 = 2 \\
  2\pi R2 = 8 \pi \\
  => R2 = 4 \\
  \text{Original Area =} 4\pi * 2^2 \\
  = 16 \pi \\
  \text{New Area =} 4\pi * 4^2 \\
  = 64 \pi
  \end{aligned}
  
  So the area quadruples.
  

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• 30. The area of incircle of an equilateral triangle of side 42 cm is :

  1. \begin{aligned} 462 cm^2 \end{aligned}
  2. \begin{aligned} 452 cm^2 \end{aligned}
  3. \begin{aligned} 442 cm^2 \end{aligned}
  4. \begin{aligned} 432 cm^2 \end{aligned}

  Answer And Explanation

  Answer: Option A

  Explanation:

  \begin{aligned}
  \text{Radius of incircle} = \frac{a}{2\sqrt3} \\
  = \frac{42}{2\sqrt3} \\
  = 7\sqrt{3} \\
  \text{Area of incircle =} \\
  \frac{22}{7}*49*3 = 462 cm^2
  \end{aligned}

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• 31. There is a plot which is rectangular in shape and it area is 460 square metres. What will be breadth of the plot if length of plot is 15% more than the breadth of plot ?

  1. 8 mtr
  2. 10 mtr
  3. 15 mtr
  4. 20 mtr

  Answer And Explanation

  Answer: Option D

  Explanation:

  \begin{aligned} l*b = 460 m^2 \end{aligned} .. (i)
  Lets suppose breadth of plot is = b rnLength will be,\begin{aligned}l=b*\frac{100+15}{100}\\=\frac{115b}{100}\end{aligned} .. (ii)
  
  From (i) and (ii), we get :
  \begin{aligned}
  \frac{115b}{100}*b = 460 \\
  b^2 = \frac{46000}{115} = 400 \\
  => b = \sqrt{400} = 20 meter
  \end{aligned}

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