Area of a Circle

Q.

An athlete completes one round of a circular track of diameter $200\mathrm{m}$ in $40\mathrm{s}.$ What will be the distance covered and the displacement at the end of $2\min 20\mathrm{s}?$

Q.

How is land distributed between the farmers of Palampur?

Q.

Recall, $\mathrm{\pi }$ is defined as the ratio of the circumference (say $\mathrm{c}$) of a circle to its diameter, (say $\mathrm{d}$) . That is, $\mathrm{\pi }=\frac{\mathrm{c}}{\mathrm{d}}$. This seems to contradict the fact that $\mathrm{\pi }$ is irrational. How will you resolve this contradiction?

Q. If the perimeter of a square and the circumference of a circle are equal, then the area of the square is ________ the area of the circle.

1. greater than
2. twice
3. half
4. less than

Q.

The circumference of the circle is $132cm$; find its area.

Q. Question 7
Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions $25cm\times 20cm\times 5cm$ and the smaller of dimension $15cm\times 12cm\times 5cm$. For all the overlaps, $5\%$ of the total surface area is required extra. If the cost of the cardboard is $Rs.4for1000c{m}^2$, find the cost of cardboard required for supplying 250 boxes of each kind.

Q.

How do you prove that the circumference of a circle is $2\mathrm{\pi }r$?

Q.

The radius of a circle is stated as $2.12cm.$ Its area should be written as

Q. What is radius of curvature of projectile motion?

Q.

Find the area of the circle whose diameter is 10m. Express your answer in ${cm}^2$. [2 MARKS]

Q. Two cross road each of width 10m cut at right angles through the centre of a rectangular park of length 700m and breadth 300m and parallel to its sides .find the area of the roads.also find the area of the park excluding the crossroads in hectares.

Q.

Question 13
A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? $(Take\pi =3.14)$

Q.

Find the area of the following circle given that$:$ radius$=30cm$

Q.

Length and breadth of a piece of rectangular wire are 18 cm and 15 cm. It is bent into the shape of a circle . find the diametre of the circle

Q.

The volumes of two spheres are in the ratio $64:27$. Find the difference of their surface area if the sum of their radii is $7cm$.

Q.

The length of the equator of the globe is $44\mathrm{cm}$. Find its surface area.

Q.

Radius of the outer circle is 18 cm and the radius of the inner circle is 7 cm. What is the area of the region between the outer and the inner circles?

1. 361π cm²

2. 192.5 cm²

3. 133 cm²

4. 275π cm²

Q.

The minute hand of a circular clock is 14 cm. How far does the tip of the minute hand move in 1 hour?

Q.

Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

Q.

A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
$[Assume\pi =\frac{22}{7}]$

Q.

How many times a circular wheel of diameter 56 CM must rotate to go 704 m?

Q. Find the area of the circle with radius $7m$. Take $\pi =\frac{22}{7}$.

1. $154m^2$
2. $308m^2$
3. $310m^2$

Q.

The side of given square is equal to twice the radius of the circle. Which of them will have greater area?
[3 MARKS]

Q.

Find the area of a triangle whose sides are 48cm, 14cm and 50 cm.

1. 305 $c{m}^2$

2. 336 $c{m}^2$

3. 265 $c{m}^2$

4. 330 $c{m}^2$

Q.

A farmer has a rectangular field of length and breadth $250m$and $160m$ respectively.He wants to fence it with $4$rounds of barbed wire .What is the total length of barbed wire to be used in fencing ?

Q. Area of a semicircle is 308 $c{m}^2$, then find its diameter.

1. 14 cm
2. 21 cm
3. 28 cm
4. 49 cm

Q.

If the diameter of a circle is $20\mathrm{cm}$, what is the area?

Q.

Radius of a circle is doubled. What will be the ratio between the area of the new circle and the area of the original circle?

1. 5:3

2. 2:3

3. 4:8

4. 4:1

Q.

A car has two wipers which do not overlap. Each wiper has a blade of length $25$ cm sweeping through an angle of $115°$. Find the total area cleaned at each sweep of the blades.

Q.

Observe the shapes 1, 2, 3 and 4 in the figure. Which of the following statements is not correct?

1. Shapes 1 and 4 have the same area as well as the same perimeter.

2. Shapes 1, 2 and 4 have the same area.

3. Shapes 1, 3 and 4 have different areas and different perimeters.

4. Shapes 1, 3 and 4 have the same perimeter.