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QUESTION: 1

If a square is inscribed in a circle, then the ratio of their areas is

Solution:

Let side of square be x cms inscribed in a circle.

Radius of circle (r) = 1/2(diagonal of square)

QUESTION: 2

In the given figure, O is the centre of the circle, and AC is its diameter. Another circle with AB as diameter is drawn. If AC = 54 cm and BC = 10 cm, the area of shaded portion will be

Solution:

AC=54cm, Radius=AO=54/2=27cm

Area of the bigger circle= πR^{2}= 22/7 * 27 * 27=2291 (approx)

Diameter of the smaller circle=54-10=44

Radius=44/2=22

Area of the smaller circle= πr^{2}=22/7 * 22 * 22=1521 (approx)

Area of the shaded region=Area of the bigger circle-Area of the smaller circle

= 2291-1521=770 cm^{2}

QUESTION: 3

The perimeter of the given figure is

Solution:

Perimeter is the boundary of the figure

So we have two semicircles of radius 14cm which makes one complete circle. Also there are two semicircles of radius 7 cm which makes one circle.

So perimeter= 2πR+2πr=2(R+r)=2*22/7(14+7)=22*6=132cm

QUESTION: 4

If PQRS is a square of side 14 cm and PAQ and SAR are semi-circles, then the area of the shaded region is

Solution:

QUESTION: 5

What is the area of the square inscribed in a circle with a circumference of 18.84 cm?

Solution:

QUESTION: 6

A park is in the form of a rectangle 120m by 90 m. At the centre of the park there is a circular lawn as shown in the figure. If the area of the park excluding the lawn is 2950 m^{2}, then the radius of the circular lawn will be

Solution:

**ANSWER :- b**

**Solution :- Area of rec. park=(120×90)m²=10800m²**

**Area of rec. park excluding lawn=2950m²**

**Area of circular lawn=(10800 - 2950)m²**

**=7850m²**

**Let the radius be = r**

**7850/3.14 = 3.14r²/3.14**

**→2500 = r²**

**→√2500 = √r²**

**→50 = r**

**→r = 50**

**Radius = 50m**

QUESTION: 7

Calculate the area of the designed region in the given figure common between the two quadrants of circles of radius 8 cm each.

Solution:

QUESTION: 8

From a circular sheet of paper with a radius 20 cm, four circles of radius 5 cm each are cut out. What is the ratio of the uncut to the cut portion?

Solution:

Four circles of radius 5 cm are cut out.

Area cut = 4*(π5^{2}) = 100π

Total area of circular sheet = π(20)^{2} = 400π

Area uncut = 300 π

The ratio of uncut to cut portion is 3 : 1

QUESTION: 9

A momento is made as shown in the figure. Its base, shade is to be silver plated from the front at the rate of rs 20 per cm^{2}. What is the total cost of silver plating?

Solution:

QUESTION: 10

In given figure, a circle of radius 7.5cm is inscribed in a square, the remaining area of the square is

Solution:

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