Master Mensuration: The 5-Second Square to Circle Area Shortcut

Question 1

A square is inscribed in a circle of radius 'r'. What is the area of the square?

MCQ

2r² πr² s²/2 r²

Question 2

If the circumference of a circle is increased from 4π to 8π, what happens to its area?

MCQ

It doubles It remains same It quadruples It triples

Question 3

The perimeter of a square and a circle are equal. Which shape encloses more area?

MCQ

Both are equal Square Circle Cannot be determined

Question 4

A circular track has a radius of 70 m. What is the distance covered by a cyclist in 10 rounds?

MCQ

4400 m 2200 m 440 m 700 m

Question 5

How many circles of radius 7 cm can be cut from a rectangular sheet of 28 cm x 14 cm?

MCQ

1 8 4 2

Question 6

If the area of a circle is 1386 cm², and the wire is reshaped into a square, what will be the area of the square?

MCQ

1000 cm² 1156 cm² 1089 cm² 1210 cm²

Question 7

A wire bent into a square encloses an area of 484 cm². If the same wire is bent into a circle, what is the area of the circle?

MCQ

616 cm² 600 cm² 584 cm² 644 cm²

Question 8

A wire of length 88 cm is bent into a circle. Find the area of the circle.

MCQ

616 cm² 462 cm² 308 cm² 154 cm²

Question 9

The diagonal of a square is 10 cm. Find its area.

MCQ

25 cm² 100 cm² 50 cm² 20 cm²

Question 10

A horse is tied to a pole in a square field of side 30m with a 14m long rope. What is the area the horse can graze?

MCQ

154 m² 308 m² 44 m² 616 m²

Question 11

If the radius of a circle is decreased by 50%, what is the percentage decrease in its area?

MCQ

50% 25% 100% 75%

Question 12

If the side of a square is doubled, by how many times does its area increase?

MCQ

4 times 8 times 2 times 3 times

Question 13

The area of a square is equal to the area of a circle. What is the ratio of the side of the square to the radius of the circle?

MCQ

1 : π sqrt(π) : 1 1 : sqrt(π) π : 1

Question 14

If the numerical value of the area of a circle is equal to its circumference, find its radius.

MCQ

4 units π units 1 unit 2 units

Question 15

The ratio of the radii of two circles is 2:3. What is the ratio of their areas?

MCQ

4:9 2:3 sqrt(2):sqrt(3) 8:27