The given figure is made up of a big semicircle and 3 identical small semicircle. Given the radius of the small semicircle r is 5 cm, find the area of the shaded region. Use 3.14 to approximate.
To find the area of the shaded region, we first need to find the radius of the big semicircle. Since the small semicircle has a radius of 5 cm, the diameter of each small semicircle is 10 cm.
To find the radius of the big semicircle, we can draw a line from the center of the big semicircle to the midpoint of the diameter of one of the small semicircles. This line will be the radius of the big semicircle.
The radius of the big semicircle is half the diameter of one of the small semicircles, so the radius of the big semicircle is 10/2 = 5 cm.
Now we can find the area of the shaded region.
The area of the big semicircle is given by (1/2)(pi)(r^2), where r is the radius. Substituting in the radius of 5 cm, we have:
(1/2)(3.14)(5^2) = (1/2)(3.14)(25) = 39.25 cm^2.
The total area of the three small semicircles is given by 3 times the area of one small semicircle: 3(1/2)(pi)(r^2) = 3(1/2)(3.14)(5^2) = 3(1/2)(3.14)(25) = 94.5 cm^2.
The area of the shaded region is the area of the big semicircle minus the total area of the three small semicircles: 39.25 cm^2 - 94.5 cm^2 = -55.25 cm^2.
However, the area can't be negative, so there must be an error in the calculations or the diagram provided. Please double-check the information given and restate the problem if necessary.