Find the diameter of a circle whose area is equal to the sum of areas of 2 circles of radii 24cm and 7cm
Answers
Radius of two circles are 24 cm and 7 cm.
Thus, area of two circles
= pi x (24)2 + pi (7)2
= pi x (576 + 49)
=pi x (625)
Now, pi(625 is the area of circle that is equal to the sum of the area of two circles.
Thus, we have
pi x (625) = pi (r2)
i.e. r2 = 625
i.e. r = 25
Hence, diameter = 2r = 2 x 25 = 50 cm
^_^
Answer:
We have the formula for area of circle,
Area=\pi \ r^2Area=π r
2
, where rr is the radius of the circle
Let, the circle whose area is equal to the sum of the areas of the two circles of radii 24 \ cm24 cm and 7 \ cm7 cm be A_3A
3
and its radius be r_3r
3
Area of circle with radius,r_1=24 \ cmr
1
=24 cm be A_1A
1
Area of circle with radius,r_2=7 \ cmr
2
=7 cm be A_2A
2
Given,
A_3=A_1+A_2A
3
=A
1
+A
2
\pi (r_3)^2=\pi(r_1)^2+\pi(r_2)^2π(r
3
)
2
=π(r
1
)
2
+π(r
2
)
2
\pi (r_3)^2=\pi[(r_1)^2+(r_2)^2]π(r
3
)
2
=π[(r
1
)
2
+(r
2
)
2
]
(r_3)^2=(r_1)^2+(r_2)^2(r
3
)
2
=(r
1
)
2
+(r
2
)
2
(r_3)^2=(24)^2+(7)^2=625=25^2(r
3
)
2
=(24)
2
+(7)
2
=625=25
2
r_3=25r
3
=25
Diameter \ = \ 2 \times \ radius \ = \ 2 \times \ 25 \ = \ 50 \ cmDiameter = 2× radius = 2× 25 = 50