In the given figure , a circle of diameter 21cm is given . Inside this circle ,two circles withbdiamwter 2 divided by 3 and 1 divided by 3 of the diameter of the big circle have been drawn , as shown in the figure . find the area of the shaded region.
Answers
Area of shaded region = Area of circle with radius 21 - [ Area of circle with diameter 2/3 + Area of circle with diameter 1/3 ]
Consider the attached figure, while going through the following steps.
Area of circle = π × r²
Area of circle with radius 21 cm
Area = π × r²
= 22/7 × 21²
= 1386 cm²
Area of circle with diameter 2/3 of the diameter of the big circle
diameter of bigger circle = 2 × r = 2 × 21 = 42
d = 2/3 × (42) = 28 cm
r = 28/2 = 14 cm
Area = π × r²
= 22/7 × 14²
= 616 cm²
Area of circle with diameter 1/3 of the diameter of the big circle
d = 1/3 × (42) = 14 cm
r = 14/2 = 7 cm
Area = π × r²
= 22/7 × 7²
= 154 cm²
Area of shaded region = 1386 - [ 616 + 154 ]
= 1386 - 770
= 616 cm²
Therefore the area of shaded portion is 616 cm²
in the given figure a circle of diameter 21 cm is given inside the circle to circle with diameter 2 upon 3 and 1 upon 3 of the diameter of the big circle have been is the given figure find the area of the sudden region