H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Area Related To Circle, Exercise 6: REVISION EXERCISE

The area and circumference of a circle are numerically equal. If the radius of the circle is $k$ units, then find the value of $k$.

The radii of two circles are $4 \mathrm{cm}$ and $3 \mathrm{cm}.$ Find the radius of the circle whose area is equal to the sum of the areas of the two circles. Also find the circumference of this circle.

A semi-circular sheet of paper of diameter $28 \mathrm{cm}$ is bent into an open conical cup. Find the depth and capacity of the cup.

In figure $ABCD$ is a square of side $8 \mathrm{cm}. CBED$ and $ADFB$ are quadrants of circle. If the area of the shaded region is $k {\mathrm{cm}}^2$ then find $k$ correct up to two decimal place. $(\text{ use }\pi =\frac{22}{7})$

The length of a rope by which a cow is tethered is increased from $16 \mathrm{m}$ to $23 \mathrm{m}$. If the additional area that the cow can graze is $k {\mathrm{m}}^2$, then, find the value of $k$, considering $\mathrm{\pi }=\frac{22}{7}$.

The area of an equilateral triangle $ABC$ is $17320.5 {\mathrm{cm}}^2.$ With each vertex of the triangle as the centre, three circles are drawn with the radius equal to half the length of the side of the triangle. If the area of the shaded region is $k {\mathrm{cm}}^2$, then the value of $k$ is 

 (Use, $\pi =3.14$ and $\sqrt{3}=1.73205$)

In the figure $ABC$ is a right-angled triangle, $\angle B=90°$ $AB=28 \mathrm{cm}$ and $BC=21 \mathrm{cm}.$ With $AC$ as diameter, a semi-circle is drawn and with $BC$ as radius a quarter circle is drawn. If the area of the shaded region is $k {\mathrm{cm}}^2$, find $k$.

In figure, two circular flower beds have been shown on two sides of a square lawn $ABCD$ of side $56 \mathrm{cm}$. If the center of each circular flower bed is the point of intersection $O$ of the diagonals of the square lawn and the sum of the areas of the lawn and flower beds is $k {\mathrm{m}}^2$ then find $k$.