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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.

  • 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}

  • 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}