Relationship Between the Circumference and the Diameter of a Circle

Two tyres $A \text{and} B$  are with diameter $\frac{1}{2} \mathrm{m}$ and  $\frac{1}{4} \mathrm{m}$. Find the distance covered by tyres in one complete round.

Write the formula for the distance travelled by a circular wheel.

From a semicircle region OABCD triangle ABD in which AB = 3 cm and BD = 4 cm is removed. Find the perimeter of the remaining figure.

A man is running around a regular hexagonal field of side length $6 \mathrm{m}$, so that he always at a distance $3$ metre from the nearest boundary. Find the length of path travelled by him in one round.

In the picture below, a square is drawn with its vertices on a circle. If the perimeter of the circle is $2\mathrm{\pi }\sqrt{\mathrm{k}} \mathrm{cm}$ then find $k$.

A copper when bent in the form of a square encloses an area of $121 {\mathrm{cm}}^2$. If the same wire is bent into the form of a circle, find the area of the circle in ${\mathrm{cm}}^2$.

If the circumference of a circle which has an area of $144\mathrm{\pi } {\mathrm{cm}}^2$ is $k\mathrm{\pi }$, then find the value of $k$.

A bucket is raised from a well by means of a rope which is wound round a wheel of diameter $77 \mathrm{cm}$. Given that the bucket ascends in $1 \mathrm{minute} 28 \mathrm{seconds}$ with a uniform speed of $1.1 \mathrm{m}/\mathrm{s},$ calculate the number of complete revolutions the wheel makes in raising the bucket. (Use$\mathrm{\pi }=\frac{22}{7}$ )

The boundary of the shaded portion in Fig., consists of three semi-circular areas, the two smaller ones being equal. If the diameter of the bigger one is $56 \mathrm{cm}$, calculate the area of the shaded region.

The boundary of the shaded portion in Fig., consists of three semi-circular areas, the two smaller ones being equal. If the diameter of the bigger one is $56 \mathrm{cm}$, calculate the length of the boundary of shaded region.

A circular running track is bounded by two concentric circles. If the cost of fixing the fence along the outer circumference is $\mathrm{Rs}. 3696$at the rate of $\mathrm{Rs}. 24$ per metre and the cost of levelling the track is $\mathrm{Rs}. 6006$ at the rate of $\mathrm{Rs}. 12$ per sq metre, calculate the width of the track.

A circular racing track is bounded by two concentric circles with circumferences $220 \mathrm{m} \mathrm{and} 286 \mathrm{m}$. Calculate the area of the track.

A lawn is in the shape of a semi-circle of diameter $35 \mathrm{m}.$ The lawn is surrounded by a flower bed of width $3.5 \mathrm{m}$ all around. Find the area of the flower bed.

A road $7 \mathrm{metres}$ wide surrounds a circular park of circumference $704 \mathrm{meters}$. Find the area of the road.

A garden roller has a circumference of 3.3 m. How many revolutions it makes in moving 231 metres?

The diameter of a cycle wheel is $35 \mathrm{cm}$. How many revolutions will it make in moving $3.3 \mathrm{km}$ ?

Fig. shows the inner boundary of a $620 \mathrm{m}$running track, which has $2$ parallel straight lines, each of length $200 \mathrm{m}$ and two semi-circular ends. Taking $\mathrm{\pi }=\frac{22}{7}$. calculate the radius of each semi-circular end.

Find the area of a circle whose circumference is $88 \mathrm{cm}.$ [Write the answer in numericals without units]

Find the circumference of a circle of area $301.84 {\mathrm{cm}}^2$.

The circumference of a circular garden is $572 \mathrm{m}$. Outside the garden a road, $3.5 \mathrm{m}$ wide runs around it. Calculate the cost of repairing the road at the rate of Rs. $375$ per $100$ sq m.