Answer
Verified
379.2k+ views
Hint: In the given question, we have to find the area of the road. In one revolution, the road roller will cover an area equal to its lateral surface. Since the road roller is in the shape of a cylinder, we can find the lateral surface area with the help of formula \[2\pi rh\] and multiply with the number of revolutions to get the area of the road.
Complete step by step solution:
In this given problem,
Road-roller is used to level the ground and its wheels are generally in the shape of a cylinder. It is shown in diagram as follows:
The formula for lateral surface area of cylinder is:
\[ = 2\pi rh\] ---------(1)
We are given that-
\[h = 1m = \] height or length of the cylinder
\[
r = \dfrac{{Diameter}}{2} = \dfrac{{84}}{2}cm \\
= 42cm \;
\]
Therefore, Radius of the cylinder, \[r = \dfrac{{42}}{{100}}m\]
Substitute all values in the formula, the lateral surface area of road roller will be:
\[ \Rightarrow 2\pi rh = 2(\dfrac{{22}}{7})(\dfrac{{42}}{{100}})(1)\]
\[ = 2.64{m^2}\]
Now the area of the road will be total revolutions completed by the road-roller multiplied by the LSA of road-roller:
\[ = 750 \times 2.64\]
\[ = 1980{m^2}\]
Thus, the area of the road is \[1980{m^2}\].
So, the correct answer is “\[1980{m^2}\]”.
Note: The key point in this question is to identify the formula and shape of the road roller.
A cylinder is one of the most common three-dimensional shapes, with two parallel circular bases separated by a space.
A curved surface connects the two circular bases at a fixed distance from the middle. The axis of the cylinder is a line segment that connects the centres of two circular bases. The height of the cylinder is the distance between the two circular bases. Example – LPG cylinder.
Complete step by step solution:
In this given problem,
Road-roller is used to level the ground and its wheels are generally in the shape of a cylinder. It is shown in diagram as follows:
The formula for lateral surface area of cylinder is:
\[ = 2\pi rh\] ---------(1)
We are given that-
\[h = 1m = \] height or length of the cylinder
\[
r = \dfrac{{Diameter}}{2} = \dfrac{{84}}{2}cm \\
= 42cm \;
\]
Therefore, Radius of the cylinder, \[r = \dfrac{{42}}{{100}}m\]
Substitute all values in the formula, the lateral surface area of road roller will be:
\[ \Rightarrow 2\pi rh = 2(\dfrac{{22}}{7})(\dfrac{{42}}{{100}})(1)\]
\[ = 2.64{m^2}\]
Now the area of the road will be total revolutions completed by the road-roller multiplied by the LSA of road-roller:
\[ = 750 \times 2.64\]
\[ = 1980{m^2}\]
Thus, the area of the road is \[1980{m^2}\].
So, the correct answer is “\[1980{m^2}\]”.
Note: The key point in this question is to identify the formula and shape of the road roller.
A cylinder is one of the most common three-dimensional shapes, with two parallel circular bases separated by a space.
A curved surface connects the two circular bases at a fixed distance from the middle. The axis of the cylinder is a line segment that connects the centres of two circular bases. The height of the cylinder is the distance between the two circular bases. Example – LPG cylinder.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
How do you graph the function fx 4x class 9 maths CBSE
Which are the Top 10 Largest Countries of the World?
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
The largest tea producing country in the world is A class 10 social science CBSE
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE