The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 π cm 2 , find the area of the smaller circle.

Let the two radii of two circles be 3a and 8a. The difference between their areas = 2695 π cm 2 ⇒ π x (8a) 2 \- π x (3a) 2 = 2695 π ⇒ π x 64a 2 \- π x 9a 2 = 2695 π ⇒ π x (64a 2 \- 9a 2 ) = 2695 π ⇒ x (64a 2 \- 9a 2 ) = 2695 ⇒ 64a 2 \- 9a 2 = 2695 ⇒ 55a 2 = 2695 ⇒ a 2 = ⇒ a 2 = 49 ⇒ a = ⇒ a = 7 cm The radii are 3a and 8a = 3 x 7 cm and 8 x 7 cm = 21 cm and 56 cm Area of smaller circle = π x (21) 2 Hence, the area of smaller circle is 1,386 cm 2 .

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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 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.

Mensuration

Related Questions

A circle of largest area is cut from a rectangular piece of card-board with dimensions 55 cm and 42 cm. Find the ratio between the area of the circle cut and the area of the remaining card-board.

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 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.

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

Mathematics

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.

Mensuration

Related Questions

A circle of largest area is cut from a rectangular piece of card-board with dimensions 55 cm and 42 cm. Find the ratio between the area of the circle cut and the area of the remaining card-board.

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 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.

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

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.

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.