PSLE The figure shows a rectangle with its corners cut out. Each of the 4 identical corners cut out is a quarter circle. The ratio of the length of the rectangle to its breadth is 10 : 7.
- What is the radius of each quarter circle?
- What is the perimeter of the shaded part. Take π = 3.14. Give your answer correct to 1 decimal place.
Length of the rectangle
= 10 u
= 2 radii + 18
Breadth of the rectangle
= 7 u
= 2 radii + 3
10 u - 7 u = (2 radii) + 18 - (2 radii + 3)
3 u = 18 - 3
3 u = 15
1 u = 15 ÷ 3 = 5
7 u = 7 x 5 = 35
Radius of the quarter circle
= (35 - 3) ÷ 2
= 32 ÷ 2
= 16 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 32
= 100.48 cm
Perimeter of the shaded part
= 100.48 + 18 + 18 + 3 + 3
= 142.48 cm
≈ 142.5 cm (Correct to 1 decimal place)
Answer(s): (a) 16 cm; (b) 142.5 cm