The dimensions of a rectangle are 24 cm and 16 cm. If the circumference of the circle is 110% of the perimeter of rectangle, then what will be the area of the circle?
1. 550 cm2
2. 792 cm2
3. 616 cm2
4. 921 cm2
5. 587 cm2
The dimensions of a rectangle are 24 cm and 16 cm. If the circumference of the circle is 110% of the perimeter of rectangle, then what will be the area of the circle?
1. 550 cm2
2. 792 cm2
3. 616 cm2
4. 921 cm2
5. 587 cm2
1. 550 cm2
2. 792 cm2
3. 616 cm2
4. 921 cm2
5. 587 cm2
Correct Answer – Option 3 : 616 cm2
Given:
The dimensions of the rectangle are 24 cm and 16 cm.
The circumference of the circle = 110% of the perimeter of rectangle.
Formula Used:
Perimeter of the rectangle = 2 × (length + breadth)
Circumference of the circle = 2πr
Area of the circle = πr2
Where r = radius of the circle
Calculation:
Circumference of the circle = 110% of Perimeter of the rectangle
⇒ 2πr = (110/100) × 2 × (24 + 16)
⇒ 2 × (22/7) × r = (11/10) × 2 × 40
⇒ r = (11 × 2 × 40 × 7)/(10 × 2 × 22)
⇒ r = 14
Area of the circle = πr2
⇒ (22/7) × 142
⇒ 22 × 2 × 14
⇒ 616
∴ Area of the circle is 616 cm2.