In a rectangle with sides of 5 cm and 12 cm, three round cuts are made with radii of 1 cm, 2 cm and 3 cm.

In a rectangle with sides of 5 cm and 12 cm, three round cuts are made with radii of 1 cm, 2 cm and 3 cm. Find the sum of the lengths of the circles of these cutouts and the area of the remaining part of the rectangle.

1. Determine the sum of the lengths of the circles.

L = 2πr1 + 2πr2 + 2πr3;

L = 2π (r1 + r2 + r3);

L = 2 * 3.14 * (1 + 2 + 3);

L = 6.28 * 6;

L = 37.68 cm.

2. Determine the area of the remaining part of the rectangle.

S o.h. = S rectangle – S cutouts;

S o.h. = 5 * 12 – (πr1 ^ 2 + πr2 ^ 2 + πr3 ^ 2);

S o.h. = 60 – π (r1 ^ 2 + r2 ^ 2 + r3 ^ 2);

S o.h. = 60 – π (1 ^ 2 + 2 ^ 2 + 3 ^ 2);

S o.h. = 60 – 3.14 * (1 + 4 + 9);

S o.h. = 16.04 cm2.

Answer: the sum of the lengths of the circles is 37.68 cm, the area of the remaining part of the rectangle is 16.04 cm2.