Mensuration
- A wire when bent in the form of a square encloses an area of 484 sq. cm. What will be the enclosed area when the same wire is bent into the form of a circle? (Take π = 22/7 )
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Using Rule 10 and 14,
Area of the square = (side)²
484 sq.cm. = (side)²
Side =√484 = 22 cm
∴ Perimeter of the square = 4 × side = 4 × 22 = 88 cm
According to the question, the circle is made by same wire.
Therefore,
Perimeter of the square = circumference of the circle 88 cm = 2πr88cm = 2 × 22 × r 7 ⇒ r = 88 × 7 = 14 cm 2 × 22
∴ Area of circle = πr²= 22 × (14)² = 22 × 14 × 14 7 7
= 616 sq.cm.Correct Option: C
Using Rule 10 and 14,
Area of the square = (side)²
484 sq.cm. = (side)²
Side =√484 = 22 cm
∴ Perimeter of the square = 4 × side = 4 × 22 = 88 cm
According to the question, the circle is made by same wire.
Therefore,
Perimeter of the square = circumference of the circle 88 cm = 2πr88cm = 2 × 22 × r 7 ⇒ r = 88 × 7 = 14 cm 2 × 22
∴ Area of circle = πr²= 22 × (14)² = 22 × 14 × 14 7 7
= 616 sq.cm.
- If the area of a circle and a square are equal, then the ratio of their perimeter is
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Using Rule 10 and 14,
Let the radius of circle = r and side of square = x units, Then,Area of circle = = 2πr = √π or √π : 2 4√πr 2 Correct Option: D
Using Rule 10 and 14,
Let the radius of circle = r and side of square = x units, Then,Area of circle = = 2πr = √π or √π : 2 4√πr 2
- A copper wire is bent in the form of square with an area of 121 cm². If the same wire is bent in the form of a circle, the radius (in cm) of the circle is (Take π = 22/7)
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Using Rule 10,
Side of square = √121 = 11 cm
&there4 Length of wire = 4 × 11 = 44 cm
∴ 2πr = 44⇒ 2 × 22 × r = 44 7 ⇒ r = 44 × 7 = 7 cm. 2 × 22 Correct Option: A
Using Rule 10,
Side of square = √121 = 11 cm
&there4 Length of wire = 4 × 11 = 44 cm
∴ 2πr = 44⇒ 2 × 22 × r = 44 7 ⇒ r = 44 × 7 = 7 cm. 2 × 22
- The volume of a right circular cylinder whose height is 40cm, and circumference of its base is 66 cm, is :
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Circumference of the base, C = 2πr
where, r = radius of the base⇒ r = C 2π
Given; C = 66cm, h = 40cm Volume = πr²h= π 
C 
² h = C²h 2π 4π = 66 × 66 × 40 cm³ 4 × 22 7
= 7 × 3 × 66 × 10 cm³ = 13860 cm³Correct Option: D
Circumference of the base, C = 2πr
where, r = radius of the base⇒ r = C 2π
Given; C = 66cm, h = 40cm Volume = πr²h= π C ² h = C²h 2π 4π = 66 × 66 × 40 cm³ 4 × 22 7
= 7 × 3 × 66 × 10 cm³ = 13860 cm³
- The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is equalto
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Using Rule 10,
Required percentage increase in area = x + y + xy % 100 = 20 + 20 + 20 × 20 % 100
= 44%Correct Option: D
Using Rule 10,
Required percentage increase in area = x + y + xy % 100 = 20 + 20 + 20 × 20 % 100
= 44%
