The sum of diameters of two circles is 14 cm and the difference of their circumferences is 8 cm. Find the circumferences of the two circles.

Let radius of larger circle be R cm and smaller circle r cm. Diameter = 2R and 2r Given, sum of diameters of two circles is 14 cm ⇒ 2r + 2R = 14 ⇒ r + R = 7 ...........(1) Given, difference in circumferences is 8 cm ⇒ 2πR - 2πr = 8 ⇒ 2π(R - r) = 8 ⇒ π(R - r) = 4 ⇒ ⇒ .........(2) Adding equation 1 and 2, Substituting value of R in Eq 2 we get, Circumference of larger circle = 2πR = = 2 x 13 = 26 cm. Circumference of smaller circle = 2πr = = 2 x 9 = 18 cm. Hence, circumference of larger circle = 26 cm and smaller circle = 18 cm.

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Mathematics

The sum of diameters of two circles is 14 cm and the difference of their circumferences is 8 cm. Find the circumferences of the two circles.

Mensuration

Related Questions

In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm². The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹ 200 per m².

Find the circumference of the circle whose area is equal to the sum of the areas of three circles with radius 2 cm, 3 cm and 6 cm.

A copper wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent into the form of a circle, find the area of the circle.

Mathematics

The sum of diameters of two circles is 14 cm and the difference of their circumferences is 8 cm. Find the circumferences of the two circles.

Mensuration

Related Questions

In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm2. The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹ 200 per m2.

Find the circumference of the circle whose area is equal to the sum of the areas of three circles with radius 2 cm, 3 cm and 6 cm.

A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.

In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm². The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.

A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹ 200 per m².

A copper wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent into the form of a circle, find the area of the circle.