Area Questions and Answers

• 1. What will be the cost of gardening 1 meter boundary around a rectangular plot having perimeter of 340 meters at the rate of Rs. 10 per square meter ?

  1. Rs. 3430
  2. Rs. 3440
  3. Rs. 3450
  4. Rs. 3460

  Answer :

  Option B

  Explanation:

  In this question, we are having perimeter.
  We know Perimeter = 2(l+b), right
  So,
  2(l+b) = 340
  As we have to make 1 meter boundary around this, so
  Area of boundary = ((l+2)+(b+2)-lb)
  = 2(l+b)+4 = 340+4 = 344
  
  So required cost will be = 344 * 10 = 3440

• 2. If the ratio of the areas of two squares is 225:256, then the ratio of their perimeters is :

  1. 15:12
  2. 15:14
  3. 15:16
  4. 15:22

  Answer :

  Option C

  Explanation:

  \begin{aligned}
  \frac{a^2}{b^2} = \frac{225}{256} \\
  \frac{15}{16} \\
  <=> \frac{4a}{4b} = \frac{4*15}{4*16} \\
  = \frac{15}{16} = 15:16
  \end{aligned}

• 3. If the radius of a circle is diminished by 10%, then the area is diminished by:

  1. 200%
  2. 210%
  3. 300%
  4. 310%

  Answer :

  Option C

  Explanation:

  Let the original radius be R cm. New radius = 2R
  
  \begin{aligned}
  Area = \pi R^2 \\
  \text{New Area =} \pi {2R}^2 \\
  = 4\pi R^2 \\
  \text{Increase in area =}(4\pi R^2 - \pi R^2) \\
  = 3\pi R^2 \\
  \text{Increase percent =} \frac{3\pi R^2}{\pi R^2}*100 \\
  = 300 \%
  \end{aligned}

• 4. The difference of the areas of two squares drawn on two line segments in 32 sq. cm. Find the length of the greater line segment if one is longer than the other by 2 cm.

  1. 9 cm
  2. 8 cm
  3. 7 cm
  4. 6 cm

  Answer :

  Option C

  Explanation:

  Let the lengths of the line segments be x and x+2 cm
  then,
  \begin{aligned}
  {(x+2)}^2 - x^2 = 32 \\
  x^2 + 4x + 4 - x^2 = 32 \\
  4x = 28 \\
  x = 7 cm
  \end{aligned}

• 5. A courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is :

  1. 16000
  2. 18000
  3. 20000
  4. 22000

  Answer :

  Option C

  Explanation:

  \begin{aligned}
  \text{Number of bricks =}\frac{\text{Courtyard area}}{\text{1 brick area}} \\
  = \left( \frac{2500 \times 1600}{20 \times 10} \right) \\
  = 20000
  \end{aligned}

• 6. The wheel of a motorcycle, 70 cm in diameter makes 40 revolutions in every 10 seconds. What is the speed of the motorcycle in km/hr

  1. 30.68 km/hr
  2. 31.68 km/hr
  3. 32.68 km/hr
  4. 33.68 km/hr

  Answer :

  Option B

  Explanation:

  In this type of question, we will first calculate the distance covered in given time.
  Distance covered will be, Number of revolutions * Circumference
  
  So we will be having distance and time, from which we can calculate the speed. So let solve.
  
  Radius of wheel = 70/2 = 35 cm
  Distance covered in 40 revolutions will be
  
  \begin{aligned}
  \text{40 * Circumference } \\
  = \text{40 * 2*\pi*r } \\
  = 40 * 2* \frac{22}{7}* 35 \\
  = 8800 cm \\
  = \frac{8800}{100} m = 88 m\\
  
  \text{Distance covered in 1 sec =}\\
  \frac{88}{10} \\
  = 8.8 m \\
  
  Speed = 8.8 m/s \\
  = 8.8*\frac{18}{5} = 31.68 km/hr
  
  \end{aligned}

• 7. The base of a triangle is 15 cm and height is 12 cm. The height of another triangle of double the area having the base 20 cm is :

  1. 22 cm
  2. 20 cm
  3. 18 cm
  4. 10 cm

  Answer :

  Option C

  Explanation:

  \begin{aligned}
  \text{Area of triangle, A1 = }\frac{1}{2}*base*height \\
  = \frac{1}{2}*15*12 = 90 cm^2 \\
  \text{Area of second triangle =} 2*A1 \\
  = 180 cm^2 \\
  \frac{1}{2}*20*height = 180 \\
  => height = 18 cm
  
  
  \end{aligned}