3. The diameter of two circles are 36 cm and 20 cm respectively. Find the area of the ci
which has circumference equal to the sum of the circumferences of the two circles. A
find ratio of area of this big circle and the sum of area of two small circle.
Answers
Answer:
Correct option is
C
28 cm
Given-
The diameter of the two circles are
d
1
=36 cm⇒ radius r
1
=
2
d
1
=
2
36
cm=18 cm and
d
2
=20 cm⇒ radius r
2
=
2
d
2
=
2
20
cm=10 cm.
∴ The circumference C
1
=2πr
1
=2π×18cm=36π cm and
The circumference C
2
=2πr
2
=2π×10 cm=20π cm
So C
1
+C
2
=(36+20)π cm=56π cm.
This is the circumference C of the resulting circle.
∴C=C
1
+C
2
=56π cm
Let the radius of this circle be r.
Now, the radius of a circle =
2π
circumference
∴r=
2π
56π
cm=28 cm.
2464 cm²
98 : 53
Step-by-step explanation:
Let the radius of the required circle be 'R'.
Radius of 1st circle = d/2 = 36/2 = 18 cm
Radius of 2nd circle = 20/2 = 10 cm
As given, circumference of biggest circle = circumference of 1st circle + circumference of 2nd circle.
=> 2π(18) + 2π(10) = 2πR
=> 2π[18 + 10] = 2πR
=> 18 + 10 = R
=> 28 = R
Area of biggest circle= πR² = π(28)² = π(784) = 2464 cm²
Sum of area of 1st + 2nd circle = π(18)² + π(10)² = π(18² + 10²) = π(424)
Required ratio = π(784)/ π(424)
Required ratio = 784/424 = 98/53