Mensuration
- Four circles of equal radii are described about the four corners of a square so that each touches two of the other circles. If each side of the square is 140 cm then area of the space enclosed between the circumference of the circle is (Take π = 22/7)
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Radius of each circle = 140 = 70 cm 2
Area of the four sectors = πr²= 22 × 70 × 70 = 15400 sq. cm. 7
Area of square = (140 × 140) sq. cm. = 19600 sq. cm.
∴ Required area = (19600 – 15400) sq. cm.
= 4200 sq. cm.Correct Option: A
Radius of each circle = 140 = 70 cm 2
Area of the four sectors = πr²= 22 × 70 × 70 = 15400 sq. cm. 7
Area of square = (140 × 140) sq. cm. = 19600 sq. cm.
∴ Required area = (19600 – 15400) sq. cm.
= 4200 sq. cm.
- The perimeter of a triangle is 67 cm. The first side is twice the length of the second side. The third side is 11 cm more than the second side. Find the length of the shortest side of the triangle.
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Let the second side of triangle = x cm.
∴ First side = 2x cm.
Third side = (x + 11) cm.
∴ Perimeter of triangle = 67 cm.
⇒ 2x + x + x + 11 = 67
⇒ 4x = 67 – 11 = 56⇒ x = 56 = 14 = smallest side 4 Correct Option: B
Let the second side of triangle = x cm.
∴ First side = 2x cm.
Third side = (x + 11) cm.
∴ Perimeter of triangle = 67 cm.
⇒ 2x + x + x + 11 = 67
⇒ 4x = 67 – 11 = 56⇒ x = 56 = 14 = smallest side 4
- The radius of a wheel is 25 cm. How many rounds it will take to complete 11 km.
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Distance covered bu whole in 1 revolution circumference of wheel
= 2πr = 
2 × 22 × 25 
cm 7
∴ Required number of revolutions == 11 × 100000 × 7 = 7000 2 × 22 × 25 Correct Option: C
Distance covered bu whole in 1 revolution circumference of wheel
= 2πr = 2 × 22 × 25 cm 7
∴ Required number of revolutions == 11 × 100000 × 7 = 7000 2 × 22 × 25
- The perimeter of a semi-circular area is 18cm, then the radius is :
(using π = 22/7)
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Using Rule 14,
Perimeter of semi-circular region = 18 cm
∴ πr + 2r = 18
⇒ r (π + 2) = 18⇒ r 22 + 2 = 18 7 ⇒ r 36 = 18 7 ⇒ r = 18 × 7 = 7 = 3 1 cm 36 2 2 Correct Option: B
Using Rule 14,
Perimeter of semi-circular region = 18 cm
∴ πr + 2r = 18
⇒ r (π + 2) = 18⇒ r 22 + 2 = 18 7 ⇒ r 36 = 18 7 ⇒ r = 18 × 7 = 7 = 3 1 cm 36 2 2
- The number of revolutions, a wheel of diameter 40 cm makes in travelling a distance of 176 m, is (Take π = 22/7)
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Using Rule 7,
Distance covered in 1 revolution = Circumference of wheel= 2πr = 2 × 22 × 20cm. 7
Total distance = 176 m = 17600 cm∴ Number of revolutions = 17600 2 × 22 × 20 7 = 17600 × 7 = 140 2 × 22 × 20 Correct Option: A
Using Rule 7,
Distance covered in 1 revolution = Circumference of wheel= 2πr = 2 × 22 × 20cm. 7
Total distance = 176 m = 17600 cm∴ Number of revolutions = 17600 2 × 22 × 20 7 = 17600 × 7 = 140 2 × 22 × 20
