Circles

A square tile of length $20 \mathrm{cm}$ has four quarter circles at each corner as shown in Fig. (i). Find the area of the shaded portion. Another tile with the same dimensions has a circle in the centre of the tile [Fig. (ii)]. If the circle touches all four sides of the square tile, find the area of the shaded portion. In which tile, area of the shaded portion will be more? $($Take $\pi =3.14)$

Give the formula for the area of a circle in terms of the diameter d.

The moon is about $384000 \mathrm{km}$ from the earth and the path around the earth is nearly circular. If the length of the path described by the moon in one complete revolution is $k \mathrm{km}$, find $k$. (Take $\pi =3.14)$

A dinner plate is in the form of a circle. The circular region encloses a beautiful design as shown. The inner circumference is $352 \mathrm{mm}$ and outer is $396 \mathrm{mm}$. If the width of the circular design is $k \mathrm{mm}$, find $k$. Use $\mathrm{\pi }=\frac{22}{7}$.

`

$ABCD$ is a rectangle with length as $80 \mathrm{cm}$ and breadth as $60 \mathrm{cm}$. $P, Q, R, S$ are the mid points of sides $AB, BC, CD, DA$, respectively. A circular rangoli of radius $10 \mathrm{cm}$ is drawn at the centre as shown. If the area of the shaded portion is $k {\mathrm{cm}}^2$, find $k$. Use $\mathrm{\pi }=\frac{22}{7}$.

A circle with radius $16 \mathrm{cm}$ is cut into four equal parts and rearranged to form another shape as shown in the figure.

Does the perimeter change? If it does change, by how much does it increase or decrease?

A circular pond is surrounded by a $2 \mathrm{m}$ wide circular path. If the outer circumference of the circular path is $44 \mathrm{m}$, find the inner circumference of the circular path. Also, find the area of the path. Use $\mathrm{\pi }=\frac{22}{7}$.

Priyanka took a wire and bent it to form a circle of radius $14 \mathrm{cm}$. Then, she bent it into a rectangle with one side $24 \mathrm{cm}$ long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle? Use $\mathrm{\pi }=\frac{22}{7}$.

How much distance, in meters, a wheel of $25 \mathrm{cm}$ radius will cover if it rotates $350$ times? If the answer is $k \mathrm{m}$, find $k$. Use $\mathrm{\pi }=\frac{22}{7}$.

Circumference '$\mathrm{C}$' of a circle is equal to $2\mathrm{\pi }\times$_____.

Circumference '$C$' of a circle can be found by multiplyıng diameter '$d$' with _____.

Value of $\mathrm{\pi }$ is _____ approximately.

If area of a triangular piece of cardboard is $90 {\mathrm{cm}}^2$, then the length of altitude corresponding to $20 \mathrm{cm}$ long base is _____ $\mathrm{cm}$.

Ratio of the circumference of a circle to its diameter is denoted by symbol _____.

The distance around a circle is its _____.

The area of a semicircle of radius $4\mathrm{r}$ is

If the radius of a circle is tripled, the area becomes

The area of a square is $100 {\mathrm{cm}}^2$. The circumference (in $\mathrm{cm}$ ) of the largest circle cut of it is

The circumference of a circle whose area is $81 {\mathrm{\pi r}}^2$, is

What is the radius of the largest circle that can be cut out of the rectangle measuring $10 \mathrm{cm}$ in length and $8 \mathrm{cm}$ in breadth?