Answer
Verified
409.8k+ views
Hint: To solve this question first we will have to determine which shape will form when each blade will be swept through an angle of \[{\rm{12}}0^\circ \]and then we will determine the area of the shape formed.
Complete step-by-step answer:
In this question, it is given that the blades are swept through an angle of \[{\rm{12}}0^\circ \]. Here we are going to assume that the blades have a shape of a straight line and the point through which the blade is rotated is fixed. Here we see that when each blade is rotated by an angle of \[{\rm{12}}0^\circ \]about a fixed point, then a sector of the circle will be formed. A sector of a circle is a portion of a circle enclosed by two radii and an arc. The angle between the two radii is called the central angle. In our case, the central angle for all the blades is \[{\rm{12}}0^\circ \]. So in this question we will calculate the area of the sector and we will multiply it by 2 because there are two sectors formed from two wipers. The formula for the calculation of area of sector of circle is as follows:
\[{\rm{Area of sector = }}\dfrac{1}{2}\, \times \,{r^2}\, \times \,\theta \]
Where r is the radius of the sector. In our case it is equal to the length of the wiper .B is the angle between the two radii. In our case, this angle is the angle of sweeping which is equal to \[{\rm{12}}0^\circ \].Therefore, we get
Area swept by one blade \[{\rm{ = }}\,\dfrac{1}{2}\,{\left( {21} \right)^2} \times \,\dfrac{{2\pi }}{3}\]
Therefore, the total area will be \[{\rm{ = }}\,{\rm{2}}\, \times {\rm{462}}\,c{m^2}\]
Note: We have assumed in the question that the wiper is a straight line with no width. If there is a width given, then we have to consider the area of the wiper also.
Complete step-by-step answer:
In this question, it is given that the blades are swept through an angle of \[{\rm{12}}0^\circ \]. Here we are going to assume that the blades have a shape of a straight line and the point through which the blade is rotated is fixed. Here we see that when each blade is rotated by an angle of \[{\rm{12}}0^\circ \]about a fixed point, then a sector of the circle will be formed. A sector of a circle is a portion of a circle enclosed by two radii and an arc. The angle between the two radii is called the central angle. In our case, the central angle for all the blades is \[{\rm{12}}0^\circ \]. So in this question we will calculate the area of the sector and we will multiply it by 2 because there are two sectors formed from two wipers. The formula for the calculation of area of sector of circle is as follows:
\[{\rm{Area of sector = }}\dfrac{1}{2}\, \times \,{r^2}\, \times \,\theta \]
Where r is the radius of the sector. In our case it is equal to the length of the wiper .B is the angle between the two radii. In our case, this angle is the angle of sweeping which is equal to \[{\rm{12}}0^\circ \].Therefore, we get
Area swept by one blade \[{\rm{ = }}\,\dfrac{1}{2}\,{\left( {21} \right)^2} \times \,\dfrac{{2\pi }}{3}\]
\[{\rm{ = }}\,\dfrac{1}{2}\,21\, \times \,21\, \times \,\dfrac{2}{3}\, \times \,\dfrac{{22}}{7}\]
\[{\rm{ = }}\,462\,c{m^2}\]
Therefore, the total area will be \[{\rm{ = }}\,{\rm{2}}\, \times {\rm{462}}\,c{m^2}\]
\[{\rm{ = }}\,924\,c{m^2}\]
Note: We have assumed in the question that the wiper is a straight line with no width. If there is a width given, then we have to consider the area of the wiper also.
Recently Updated Pages
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with proper collective nouns 1 A of class 10 english CBSE
What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Net gain of ATP in glycolysis a 6 b 2 c 4 d 8 class 11 biology CBSE
What organs are located on the left side of your body class 11 biology CBSE