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 5 : 3.
- 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
= 5 u
= 2 radii + 23
Breadth of the rectangle
= 3 u
= 2 radii + 7
5 u - 3 u = (2 radii) + 23 - (2 radii + 7)
2 u = 23 - 7
2 u = 16
1 u = 16 ÷ 2 = 8
3 u = 3 x 8 = 24
Radius of the quarter circle
= (24 - 7) ÷ 2
= 17 ÷ 2
= 8.5 cm
(b)
Perimeter of the 4 quarter circles
= 3.14 x 17
= 53.38 cm
Perimeter of the shaded part
= 53.38 + 23 + 23 + 7 + 7
= 113.38 cm
≈ 113.4 cm (Correct to 1 decimal place)
Answer(s): (a) 8.5 cm; (b) 113.4 cm