Lakshya Education MCQs

Question: A man is walking in a circular park. In one round he completes 314 m. If there is a man at the opposite end of the diameter which is drawn from the point where the man is standing. Find the minimum distance he has to walk to meet his friend who is sitting at the described point? Also, find the area of the circular park. Take π=3.14         [3 MARKS]
Options:

: Steps: 1 Mark
Shortest Distance: 1 Mark
Area: 1 Mark

If the man has to cover the minimum distance, he has to walk along the diameter. Circumference of the circle= 314 m Radius of the given circle= 3142π = 50 m Diameter= (2)×(50)= 100 m
The radius of the circular park = 1002 = 50 m


The area of the circular park = π×r2

On substituting the values, we get
Area =π×502 = 7850m2

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More Questions on This Topic :

Question 1. Find the area of the shaded portion. A circle is inscribed in a square such that both their centres coincide. BDE is an isosceles triangle. The side of a square is 10m.

[4 MARKS]

 

: Formula: 1 Mark
Steps: 1 Mark
Application: 1 Mark
Answer: 1 Marks

Given that,
The side of the square ABCD = 10 m.
Now the diameter of the circle will be equal to the side of the square ABCD =10 m.

Area of the square = a2
Area of the square is (10)
× (10)= 100 m2 Given diameter of circle = 10 m Radius of the circle= 102 = 5 m Area of the circle = π× (r2)
=π× (52) = 78.5m2 Area of the triangle BDE = 12× (BD)×(DE) =0.5× (10)×(10) = 50 m2 Area of the shaded region = Area of square ABCD - Area of circle + Area of triangle BDE =71.5 m2

So, the area of the shaded region is71.5 m2.
Question 2. The radius of a circle is 10 meters. Find the area of the circle in m2 , Take π = 3.14   [2 MARKS]

: Formula: 1 Mark
Answer: 1 Mark

Area of the circle of radius Ris π×R2 Radius of the given circle = 10 m Area of the given circle = π×102
= 314 m2
The area of the circle is314 m2.
Question 3. Find the perimeter of a square of side 10m. Express your answer in cm.  [1 MARK]

: Result : 1 Mark

Let the square given be of side A cm.
Perimeter of the square whose side is A cm is 4× A Perimeter of the given square = 4× 10 = 40 m = 4000 cm
Question 4. The perimeter of a rectangular field is 50 m. If the length of the field is 13 m. Find the area of the field. [2 MARKS]

: Formula: 1 Mark
Answer: 1 Mark

Given that,
The perimeter of a rectangular field is 50 m.
The length of the field is 13 m.
Perimeter of rectangular field =2( length + breadth)
Or, Breadth=perimeter2length
Or, Breadth = 25 - 13 = 12 m

Area of rectangle = length × breadth =13×12 = 156 sq. m
The area of the rectangular field is 156 m2.
Question 5. A man wants to paint two of his walls. The cost of painting is Rs10 per cm2How much money is required by him to paint a rectangular wall of length 400 cm and breadth 900 cm and a circular wall of diameter 126 cm? [4 MARKS]

: Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Given that
The cost of painting isRs10 per
cm2.
The length of the rectangular wall=400 cm
The breadth of the rectangular wall=900 cm

Area of the rectangle = length
× breadth
On substituting the values we get Area of the rectangle= (400)× (900) = 360000 cm2 Money required to paint the rectangular wall = (10)× (360000) = Rs.3600000

The diameter of the circular wall = 126 cm.
Radius of the wall, r = 1262 = 63 cm
The area a circle is given by, Area = π×r2
On substituting the values we get,
Area of the circular wall
= 227×63×63 = 12474 cm2

Money required to paint the circular wall
= 12474×10 = Rs 124740

The total cost of painting
=3600000 +124740 = Rs 3724740

Hence, the total cost of painting the walls is Rs37,24,740.
Question 6. Find the height ‘x’ if the area of the parallelogram is 24 cm2 and the base is 4cm.  [2 MARKS]

: Formula: 1 Mark
Answer: 1 Mark

Given that,
Area of a parallelogram is 24 cm2
Area of parallelogram = Base × height
Or, Height = AreaBase
On substituting the values, we get
Height = 244 = 6 m
So, the height of the parallelogram is 6 m.

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