1 Marks Question

Question 11 Mark

If the numerical value of the area of a circle is equal to the numerical value of its circumference, find its radius.

Answer

$\because$ Numerical value of area of circle = Numerical value of circumference
$\therefore$ $\pi\text{r}^2=2\pi\text{r}$
or r = 2 units

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Question 21 Mark

Write the formula for the area of a sector of angle $\theta$ (in degrees) of a circle of radius r.

Answer

Area of a sector of a circle whose radius = r
and angle at centre $=\theta,$ Will be $\pi\text{r}^2\times\frac{\theta}{360^\circ}$

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Question 31 Mark

If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?

Answer

We have the following situation

Let BD be the diameter and diagonal of the circle and the square respectively. We know that area of the circle $=\pi\text{r}^2$ Area of the square = side$^2$ As we know that diagonal of the square is the diameter of the square. Diagonal = 2r Side of the square $=\frac{\text{diagonal}}{\sqrt{2}}\ \dots(1)$ Substituting Diagonal = 2r in equation (1) we get, Side of the square $=\frac{2\text{r}}{\sqrt{2}}$ Now we will find the ratio of the areas of circle and square. $\frac{\text{Area of circle}}{\text{Area of square}}=\frac{\pi\text{r}^2}{\Big(\frac{2\text{r}}{\sqrt{2}}\Big)^2}$ Now we will simplify the above equation as below, $\frac{\text{Area of circle}}{\text{Area of square}}=\frac{\pi\text{r}^2}{\frac{4\text{r}^2}{2}}$ $\frac{\text{Area of circle}}{\text{Area of square}}=\pi\text{r}^2\times{\frac{2}{4\text{r}^2}}$ Hence, $\frac{\text{Area of circle}}{\text{Area of square}}=\frac{\pi}{2}$ Therefore, ratio of areas of circle and square is $\pi:2.$

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Question 41 Mark

In Fig. ABCD is a square of side 10 cm. A sector of radius 5 cm is cut out from one of the corners. Find the area of the shaded region.
(Take $\pi=3.14$)

Answer

$80.375 cm^2$

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Question 51 Mark

Find the length of the arc of a circle which subtends an angle of $60^{\circ}$ at the centre of the circle of radius 42 cm.

Answer

44 cm

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Question 61 Mark

A piece of wire 22 cm long is bent into the form of an arc of a circle subtending an angle of $60^{\circ}$ at its centre. Find the radius of the circle. (Use $\pi=22/7$)

Answer

21 cm

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Question 71 Mark

Find the area of the largest triangle that can be inscribed in a semi-circle of radius r units.

Answer

$r^2$

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Question 81 Mark

If the diameter of a semi-circular protractor is 14 cm, then find its perimeter.

Answer

36 cm

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Question 91 Mark

Find the ratio of the area of the circle circumscribing a square to the area of the circle inscribed in the square.

Answer

$2: 1$

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Question 101 Mark

How many revolutions a circular wheel of radius r metres makes in covering a distance of s metres?

Answer

$\frac{\pi b^2}{4}$

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Question 111 Mark

If the numerical value of the area of a circle is equal to the numerical value of its circumference, tind its radius.

Answer

2 units

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Question 121 Mark

Is it true to say that area of a segment of a circle is less than the area of its corresponding sector? Why?

Answer

No; it is only true for minor segment.

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Question 131 Mark

What is the area of a square inscribed in a circle of diameter p cm?

Answer

$\frac{p^2}{2} cm^2$

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Question 141 Mark

Find the area of a sector of circle of radius 21 cm and central angle $120^{\circ}$.

Answer

$462 cm^2$

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Question 151 Mark

An arc subtends an angle of $90^{\circ}$ at the centre of the circle of radius 14 cm. Write the area of minor sector thus formed in terms of $\pi$.

Answer

$49 \pi cm^2$

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Question 161 Mark

If the adjoining figure is a sector of a circle of radius 10.5 cm, what is the perimeter of the sector?
(Take $\pi=22/7$)

Answer

32 cm

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Question 171 Mark

Write the formula for the area of a segment in a circle a circle of radius r given that the sector angle is $\theta$ (in degrees).

Answer

$\left(\frac{\pi \theta}{360}-\sin \frac{\theta}{2} \cos \frac{\theta}{2}\right) r^2$

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Question 181 Mark

Write the formula for the area of a sector of angle $\theta$ (in degrees) of a circle of radius r.

Answer

$\frac{9}{360} \times \pi r^2$

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Question 191 Mark

If a square is inscribed in a circle, what is the ratio of the areas of the circle and the square?

Answer

$\pi: 2$

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Question 201 Mark

In a circle of radius 10 cm, an arc subtends an angle of 108 deg at the centre. What is the area of the sector in terms of $\pi$?

Answer

$\pi cm ^2$

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Question 211 Mark

What is the area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm?

Answer

$8.75 cm^2$

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Question 221 Mark

What is the angle subtended at the centre of a circle of radius 6 cm by an arc of length 3 $\pi$ cm?

Answer

$90^{\circ}$

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Question 231 Mark

What is the length (in terms of $\pi$) of the arc that subtends an angle of $36^{\circ}$ at the centre of a circle of radius 5 cm?

Answer

$\pi$ cm

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Question 241 Mark

Write the area of the sector of a circle whose radius is r and length of the arc is l.

Answer

$\frac{1}{2} lr$

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Question 251 Mark

If the circumference of two circles are in the ratio 2 : 3, what is the ratio of their areas?

Answer

$4: 9$

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Question 261 Mark

What is the ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal?

Answer

$4 \pi: \sqrt{3}$

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