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QUESTION: 1

If the area of a circle is 154 cm^{2}, then its perimeter is

Solution:

Given area of circle=154

⇒area of circle=πr²

=22/7 ×7×7.

=154

so radius of the circle=7cm

perimeter of circle=2πr

=2 ×22/7×7

=44cm

⇒perimeter of the circle=44 cm.

QUESTION: 2

The radii of two circles are 4 cm and 3 cm respectively. The diameter of the circle having area equal to the sum of the areas of the two circles (in cm)

Solution:

QUESTION: 3

If the circumference of a circle and the perimeter of a square are equal, the

Solution:

QUESTION: 4

The perimeter (in cm) of a square circumscribing a circle of radius a cm, is

Solution:

Side of a square circumscribing a circle of radius a cm = diameter of circle = 2a cm

∴ Perimeter of the square = 4 x 2a = 8a cm

QUESTION: 5

The perimeter of a circle is equal to that of a square, then the ratio of their areas is

Solution:

QUESTION: 6

If the area of a circle is numerically equal to twice its circumference, then the diameter of the circle is

Solution:

πr^{2} - 2πr x 2 ⇒ r = 4 ⇒ 2r = 8 units

QUESTION: 7

The area of the circle that can be inscribed in a square of side 6 cm is

Solution:

QUESTION: 8

The diameter of a wheel is 1.26 m. The distance travelled in 500 revolutions is

Solution:

Radius of the wheel = 1.26/2 = 0.63 m

Distance travelled in one revolution

∴ Distance travelled in 500 revolutions

= 500 x 3.96 = 1980 m

QUESTION: 9

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is

Solution:

Diameter of first circle = d_{1} = 36 cm

Diameter of second circle = d_{2} = 20 cm

∴ Circumference of first circle = πd_{1} = 36π cm

Circumference of second circle = πd_{2} = 20π cm

Now, we are given that,

**Circumference of circle = Circumference of first circle + Circumference of second circle**

πD = πd_{1} + πd_{2}

⇒ πD = 36π + 20π

⇒ πD = 56π ⇒ D = 56

⇒ Radius = 56/2 = 28 cm

QUESTION: 10

If the sum of the circumferences of two circles with radii R_{1} and R_{2} is equal to the circumference of a circle of radius R, then

Solution:

2π R_{1} + 2πR_{2} = 2πR

⇒ R_{1} + R_{2} = R.

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