Question

Find the area covered by the road roller of width 80cm and diameter 140cm in 40 revolutions.
(a). 130.8 ${{m}^{2}}$
(b). 143.6 ${{m}^{2}}$
(c). 141.8 ${{m}^{2}}$
(d). 140.8 ${{m}^{2}}$

Answer 1

Hint: We can consider the bottom of the road roller as a rectangle whose width is given as 80cm and the length will be the circumference of the circle whose diameter is 140cm. Then we will use the formula $\pi d$ for finding the circumference of the circle, and then we will use the formula $length\times width$ for the area of the rectangle.

Complete step-by-step answer:

We can consider the bottom of the road roller as a rectangle whose width is given as 80cm and the length will be the circumference of the circle whose diameter is 140cm.
Let’s look at the figure,

Hence, the formula for circumference of circle having d as diameter is $\pi d$
Now substituting the value of d as 140cm we get,
Using the value of $\pi =\dfrac{22}{7}$ we get,
$length=\pi \left( 140 \right)=440cm$
Now we will find the value of area of rectangle using the formula $length\times width$
Now substituting the value of length as 440 and width as 80 we get,
$Area=440\times 80=35200c{{m}^{2}}$
Now it is given that it has made 40 revolutions,
Hence, we have multiply the area by 40 and we get,
$35200\times 40=1408000c{{m}^{2}}$
Now we know that $1c{{m}^{2}}=\dfrac{1}{10000}{{m}^{2}}$
Now using to convert cm to m we get,
$1408000c{{m}^{2}}=\dfrac{1408000}{10000}{{m}^{2}}=140.8{{m}^{2}}$
Hence, option (d) is correct.

Note: The most important step was to consider the bottom of the road roller as a rectangle and then using the diameter and width to find the area of the rectangle. And the formula for circumference $\pi d$ and area of rectangle $length\times width$ must be kept in mind. One can also use the value of $\pi $ as 3.14.