Question

A child prepares a poster on ‘Save energy’ on a square sheet whose each side measures 60cm. At each corner of the sheet, she draws a quadrant of radius 17.5cm in which she shows the ways to save energy. At the center, she draws a circle of diameter 21cm and writes a slogan in it. Write the four ways by which energy can be saved. Why do we need to save energy?

Answer 1

Hint: Circle: A circle is a close two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. It is a round shaped figure. Every circle has radius and it is denoted by ‘r’.
As we know that area of circle
$ \Rightarrow A = \pi {R^2}$
Here,
A=area of circle
R=radius of circle.

Complete step-by-step answer:

Given,
Radius of quadrant, r=17.5cm
Diameter of center circle, D=21cm
As we know that radius is half of diameter, $R = \dfrac{D}{2}$
So the radius of center circle, $R = \dfrac{{21}}{2}$
Radius of center circle, R=10.5cm.
Side of the square, b=60cm
As we know that the area of square,
$ \Rightarrow {A_s} = b \times b$
Put the value in formula
$ \Rightarrow {A_s} = 60 \times 60$
$ \Rightarrow {A_s} = 3600c{m^2}$
Area of square is${A_s} = 3600c{m^2}$.
Now the area of center circle is,
As we know that the area of circle is,
\[ \Rightarrow A = \dfrac{\pi }{4}{D^2}\]
Put the value in the formula,
\[ \Rightarrow A = \dfrac{\pi }{4} \times 21 \times 21\]
Put the value of $\pi = \dfrac{{22}}{7}$ in equation.
\[ \Rightarrow A = \dfrac{{22}}{7} \times \dfrac{1}{4} \times 21 \times 21\]
Solve the equation
\[ \Rightarrow A = \dfrac{{22}}{4} \times 3 \times 21\]
\[ \Rightarrow A = \dfrac{{1386}}{4}\]
\[ \Rightarrow A = 346.5c{m^2}\]
Now calculate the area of one quadrant
Radius of quadrant, r=17.5m
Area of the quadrant=
\[ \Rightarrow {A_q} = \dfrac{\pi }{4}{r^2}\]
Put the value
\[ \Rightarrow {A_q} = \dfrac{\pi }{4} \times 17.5 \times 17.5\]
Put the value of $\pi = \dfrac{{22}}{7}$
\[ \Rightarrow {A_q} = \dfrac{{22}}{7} \times \dfrac{1}{4} \times 17.5 \times 17.5\]
\[ \Rightarrow {A_q} = 240.625c{m^2}\]
So the area of 4 quadrants
$ = 4 \times Area\,of\,one\,quadrants$
$ = 4 \times 240.625$
$ = 962.5c{m^2}$
So the area of shaded region is,
$ \Rightarrow Area{\text{ }}of{\text{ }}shaded{\text{ }}region = Area{\text{ }}of{\text{ }}square - \left( {area{\text{ }}of{\text{ }}center{\text{ }}of{\text{ }}circle{\text{ }} + {\text{ }}area{\text{ }}of{\text{ }}4{\text{ }}quadrants} \right)$
$ \Rightarrow Area{\text{ }}of{\text{ }}shaded{\text{ }}region = 3600 - \left( {346.5 + 962.5} \right)$
$ \Rightarrow Area{\text{ }}of{\text{ }}shaded{\text{ }}region = 3600 - 1309$
$ \Rightarrow Area{\text{ }}of{\text{ }}shaded{\text{ }}region = 2291c{m^2}$
Four ways to save energy.
I.Turn off all unnecessary lights.
II.Use natural resources.
III.Use smart power strips.
IV.Fix the leaky faucet.
We need to save energy: Energy conservation measures in building reduce the need for energy services and can result in increased environmental quality, national security, personal financial security and higher savings. It also lowers energy costs by preventing future resource depletion.
So, the correct answer is “$2291\;c{m^2}$”.

Note: The coordinate axis divides the circle into the four parts known as quadrants. Labelled them as first, second, third and fourth. Energy saving electronic equipment is also used to save the energy. Energy will be used for sustainability from one source to another.