Step-by-step explanation:
remember, the area of a whole circle (360°) is
pi×r²
r being the radius (half is the diameter).
so in circle B the radius is 48/2 = 24 meters.
the shaded area (with the 90° angle or "right angle") represents only a part of the whole circle : 90° out of the total of 360°.
so, the area is
pi×24²×90/360 = pi×576/4 = pi×144 = 452.3893421... m²
≈ 452.4 m²
for the question about circle P and the segment AB I don't have any graphic or so. but the answer is general :
since a whole circle is 360°, then a half-circle (the arc between the endpoints of the diameter) represents 360/2 = 180°.
about the circle A
remember the circumference of a whole circle (360°) is
2×pi×r
so, in our case r = 15 in
and we don't need the length of the full circumference but only of 110° out of the total of 360°.
so,
LG = 2×pi×15×110/360 = 2×pi×110/24 = pi×110/12 =
= pi×55/6 = 28.79793266... in
≈ 28.8 in
for the circle R
the angle J is the angle UJN = 28°.
this is per rule of inscribed angles half the arc angle URN.
so, the angle URN = 2×28 = 56°.
but we need only the angle URL.
the angle URL = angle URN - angle LRN.
the angle LRN is the mirrored version of the angle JRM = 21°.
so, the angle URL = 56 - 21 = 35°.
