Answer
Verified
420.9k+ views
Hint: Considering the wheel as a circle, suppose wheel makes 1 revolution then the distance travelled by the wheel in 1 revolution will be equal to the perimeter of the wheel i.e circumference of circle, using formula we can find circumference of circle i.e wheel, then the total distance covered in 5000 revolutions will be 5000 multiplied by perimeter of the wheel which is required answer.
Complete step-by-step answer:
Let us consider that the radius of the wheel is ‘r’ cm.
So, the perimeter of the wheel may be written as:
Perimeter of the wheel = $2\times \pi \times r$
Now, since the total number of revolutions made by the wheel is 5000, so the total distance travelled by the wheel in these 5000 revolutions will be =$5000\times 2\pi r=10000\pi r.........(1)$
Now, it is also given that the wheel has covered a total distance of 11 km in these 5000 revolutions.
Here, we may convert the given distance from ‘km’ to ‘cm’.
So, we know that 1 km = 100000 cm
Therefore, 11 km = 11 × 100000 cm
= 1100000 cm
So, we have the total distance covered by the wheel = 1100000 cm ………….(2)
Therefore, on comparing equation (1) and equation (2), we get:
10000×π×r cm = 1100000 cm
$\pi r=\dfrac{1100000}{10000}cm$
$r=\dfrac{110}{\pi }cm$
$r=\dfrac{110}{\dfrac{22}{7}}cm$
$r=\dfrac{770}{22}cm$
r = 35 cm
Now, we have found the radius of the wheel, so the diameter of the wheel is 2 times the radius.
So, $d=2\times r$
= 70 cm
Hence, (D) 70 cm is the correct option.
Note: Here we may have chances of mistakes due to unit conversion. Since, the distance covered is given in km and options for diameter are given in cm, so the unit from km to cm should be converted properly here.For these types of problems by applying basic geometry we can approach the solution.So,students should remember basic formulas and definitions of geometry.
Complete step-by-step answer:
Let us consider that the radius of the wheel is ‘r’ cm.
So, the perimeter of the wheel may be written as:
Perimeter of the wheel = $2\times \pi \times r$
Now, since the total number of revolutions made by the wheel is 5000, so the total distance travelled by the wheel in these 5000 revolutions will be =$5000\times 2\pi r=10000\pi r.........(1)$
Now, it is also given that the wheel has covered a total distance of 11 km in these 5000 revolutions.
Here, we may convert the given distance from ‘km’ to ‘cm’.
So, we know that 1 km = 100000 cm
Therefore, 11 km = 11 × 100000 cm
= 1100000 cm
So, we have the total distance covered by the wheel = 1100000 cm ………….(2)
Therefore, on comparing equation (1) and equation (2), we get:
10000×π×r cm = 1100000 cm
$\pi r=\dfrac{1100000}{10000}cm$
$r=\dfrac{110}{\pi }cm$
$r=\dfrac{110}{\dfrac{22}{7}}cm$
$r=\dfrac{770}{22}cm$
r = 35 cm
Now, we have found the radius of the wheel, so the diameter of the wheel is 2 times the radius.
So, $d=2\times r$
= 70 cm
Hence, (D) 70 cm is the correct option.
Note: Here we may have chances of mistakes due to unit conversion. Since, the distance covered is given in km and options for diameter are given in cm, so the unit from km to cm should be converted properly here.For these types of problems by applying basic geometry we can approach the solution.So,students should remember basic formulas and definitions of geometry.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE