Embibe Experts Solutions for Chapter: Areas Related to Circles, Exercise 1: Exercise

Raju is a table designer, his speciality is remodeling old tables. While he was remodeling an old round table, of diameter $112 \mathrm{cm}$, he planned to leave the old design, which is in the form of a regular hexagon in the center untouched, as Raju admired its craftsmanship on it. He redesigned the remaining portion of the tabletop at the rate of $₹8 \mathrm{per} 15 {\mathrm{cm}}^2$. Find the cost of redesigning (use $\sqrt{3}=1.73$ and $\mathrm{\pi }=\frac{22}{7}$)

For an average driver, research says that, there is a difference in fuel efficiency when driving with larger tyres. To apply this practically, a car company has changed the diameter of each wheel of their newly launched car model from the standard size to $42 \mathrm{cm}$.

Each wheel of this car makes $20$ revolutions in $12$ seconds. Find the speed of the new car in metre per minute.

The Gujarati Stitch is a signature stitching art of the tribal community of Kutch District in Gujarat, India. A beautiful representation of the Gujarati stitch is:

The stitch converted to a geometrical figure will look something like this:

The area of the white region is$?$  [Assume $\mathrm{\pi }=3.14, \sqrt{3}=1.732$]

Sides of a triangular field are $15 \mathrm{m}, 16 \mathrm{m}$ and $17 \mathrm{m}$. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length $7 \mathrm{m}$ each to graze in the field.

The area of the fields which cannot be grazed by the three animals is $?$ [Use, $\mathrm{\pi }=\frac{22}{7}$]

A grass field is in the form of an equilateral triangle of sides $48 \mathrm{m}$. A cow can tether at a vertex of the field. If the cow can reach up to $21 \mathrm{m}$ from the vertex, find the increase in grazing area if the length of the rope is increased to $31.5 \mathrm{m}$. [Use, $\mathrm{\pi }=\frac{22}{7}$]

In a square sheet of side $10 \mathrm{cm}$, by taking every side of the square as the diameter four semicircles are drawn, and the intersection of those four semicircles are painted with pink colour and the remaining four parts are coloured with yellow, green, red and blue as shown in the figure. Find the area of the pink coloured region (Take $\mathrm{\pi }=3.14$)

Two flower beds are in the form of segments (minor) of the circle circumscribing a square shaped green garden field of side $42 \mathrm{m}$, with two opposite sides of square as the corresponding chords as shown in the figure. Find the cost of planting flowers at the rate of $₹200$ per square metre.

A child has drawn the following cartoon of a cat:

In the above figure, the sectors of the circular portion have the radius $r$, centre $O$ and containing the central angles $\theta$.

The perimeter of the shaded region is