A calf is tied with a rope of length $6 \,m$ at the corner of a square grassy lawn of side $20\, m$. If the length of the rope is increased by $5.5\, m$, find the increase in area of the grassy lawn in which the calf can graze. (in $m ^{2}$)
A calf is tied with a rope of length $6 \,m$ at the corner of a square grassy lawn of side $20\, m$. If the length of the rope is increased by $5.5\, m$, find the increase in area of the grassy lawn in which the calf can graze. (in $m ^{2}$)
- A
$75$
- B
$85.725$
- C
$75.625$
- D
$80.500$
Similar Questions
In a circle with radius $21\,cm ,$ the perimeter of a minor sector is $64\,cm .$ Then. the length of the arc of that sector is $\ldots \ldots \ldots . . cm$.
In a circle with radius $21\,cm ,$ the perimeter of a minor sector is $64\,cm .$ Then. the length of the arc of that sector is $\ldots \ldots \ldots . . cm$.
As shown in the adjoining diagram, the length of the square plot ABCD is $50 m .$ At each vertex of the plot, a flower bed in the shape of a sector with radius $10 \,m$ is prepared. Find the area of the plot excluding the flower beds. $(\pi=3.14)$ (in $m^2$)
As shown in the adjoining diagram, the length of the square plot ABCD is $50 m .$ At each vertex of the plot, a flower bed in the shape of a sector with radius $10 \,m$ is prepared. Find the area of the plot excluding the flower beds. $(\pi=3.14)$ (in $m^2$)
The length of the minute hand of a clock is $17.5\, cm$. Find the area of the region swept by it in $15$ minutes time duration. (in $cm^2$)
The length of the minute hand of a clock is $17.5\, cm$. Find the area of the region swept by it in $15$ minutes time duration. (in $cm^2$)
Find the circumference and the area of a circular ground with radius $77\, m$.
Find the circumference and the area of a circular ground with radius $77\, m$.
Which of the following correctly matches the information given in Part $I$ and Part $II$ ?
Part $I$
Part $II$
$1.$ Formula to find the length of a minor arc
$a.$ $C=2\pi r$
$2.$ Formula to find the area of a minor sector
$b.$ $A =\pi r^{2}$
$3.$ Formula to find the area of a circle
$c.$ $l=\frac{\pi r \theta}{180}$
$4.$ Formula to find the circumference of a circle
$d.$ $A=\frac{\pi r^{2} \theta}{360}$
Which of the following correctly matches the information given in Part $I$ and Part $II$ ?
| Part $I$ | Part $II$ |
| $1.$ Formula to find the length of a minor arc | $a.$ $C=2\pi r$ |
| $2.$ Formula to find the area of a minor sector | $b.$ $A =\pi r^{2}$ |
| $3.$ Formula to find the area of a circle | $c.$ $l=\frac{\pi r \theta}{180}$ |
| $4.$ Formula to find the circumference of a circle | $d.$ $A=\frac{\pi r^{2} \theta}{360}$ |