The diameters of three circles are in the ratio 3 : 5 : 6. If the sum of the circumferences of these circles be 308 cm; find the difference between the areas of the largest and the smallest of these circles.

Let the diameters of the three circles be 3a, 5a and 6a. Radius of three circles = , and Circumference of a circle = 2πr For the first circle, r 1 = cm Circumference 1 = 2 x π x = 3aπ cm For the second circle, r 2 = cm Circumference 2 = 2 x π x = 5aπ cm For the third circle, r 2 = cm Circumference 2 = 2 x π x = 6aπ cm Total circumference = Circumference 1 + Circumference 2 + Circumference 3 ⇒ 3aπ + 5aπ + 6aπ = 308 ⇒ 14aπ = 308 ⇒ 14 x a x = 308 ⇒ 2 x a x 22 = 308 ⇒ 44a = 308 ⇒ a = ⇒ a = 7 cm Radius of three circles = x 7 cm, x 7 cm and x 7 cm = 10.5 cm, 17.5 cm and 21 cm Difference between the area of the largest and the smallest circles = π(21) 2 \- π(10.5) 2 = 441π \- 110.25π cm 2 = 330.75π cm 2 = 330.75 x cm 2 = 47.25 x 22 cm 2 = 1039.5 cm 2 Hence, the difference in the area = 1039.5 cm 2 .

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Mathematics

The diameters of three circles are in the ratio 3 : 5 : 6. If the sum of the circumferences of these circles be 308 cm; find the difference between the areas of the largest and the smallest of these circles.

Mensuration

Related Questions

The following figure shows a square card-board ABCD of side 28 cm. Four identical circles of largest possible size are cut from this card as shown below.
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Mathematics

The diameters of three circles are in the ratio 3 : 5 : 6. If the sum of the circumferences of these circles be 308 cm; find the difference between the areas of the largest and the smallest of these circles.

Mensuration

Related Questions

The following figure shows a square card-board ABCD of side 28 cm. Four identical circles of largest possible size are cut from this card as shown below.Find the area of the remaining card-board.

The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 π cm2, find the area of the smaller circle.

Find the area of a ring shaped region enclosed between two concentric circles of radii 20 cm and 15 cm.

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Find the area of the remaining card-board.

The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 π cm², find the area of the smaller circle.