R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: Exercise 16B

A wire is bent to form a square enclosing an area of $484 {\mathrm{m}}^2$. Using the same wire, a circle is formed. Find the area of the circle.

If the $k {\mathrm{cm}}^2$, then find $k$

A square $ABCD$ is inscribed in a circle of radius $r$. Find the area of the square.

If the area of the square is $k$, then find $\frac{k}{r^2}$

The cost of fencing a circular field at the rate of $₹25$ per metre is $₹5500$. The field is to be ploughed at the rate of $50$ paise per ${\mathrm{m}}^2$. Find the cost of ploughing the field. [Take$\pi =\frac{22}{7}$]

If the the cost of ploughing the field is $₹k$, find $k$

A park is in the form of a rectangle $120 \mathrm{m}$ by $90 \mathrm{m}$. At the centre of the park there is a circular lawn as shown in the figure. The area of the park excluding the lawn is $2950 {\mathrm{m}}^2$. Find the radius of the circular lawn. (given: $\pi =3.14$)

If the radius of the circular lawn is $k \mathrm{cm}$, find $k$

In the given figure, $PQSR$ represents a flower bed. If $\mathrm{OP}=21 \mathrm{m}$ and $\mathrm{OR}=14 \mathrm{m}$, find the area of the flower bed.

If the area of the flower bed is $k {\mathrm{cm}}^2$, find $k$

In the given figure $O$ is the centre of the bigger circle, and $AC$ is its diameter. Another circle with $AB$ as diameter is drawn. Also, $AC=54 \mathrm{cm}$ and $BC=10 \mathrm{cm}$, If the area of the shaded region is $k {\mathrm{cm}}^2$, then find the value of $k$. (Take $\mathrm{\pi }=\frac{22}{7}$ )

From a thin metallic piece in the shape of a trapezium $ABCD$ in which $AB\parallel CD$ and $\angle BCD={90}^o$, a quarter circle $BFEC$ is removed. Given, $AB=BC=3.5 \mathrm{cm}$ and $DE=2 \mathrm{cm}$, calculate the area of remaining (shaded) part of metal sheet in square centimetres.

If the area of the major segment $APB$ of a circle of radius $35 \mathrm{cm}$ and $\angle AOB=90°$ is $k {\mathrm{cm}}^2$, as shown in the given figure, then find the value of $k$. (Use $\mathrm{\pi }=\frac{22}{7}$)