Question

The radius of a 80 cm wide road roller is 77 cm. Calculate the number of revolutions that the roller will take to cover an area of 96.8 meter square

Answer 1

Answer:

25 revolutions

Step-by-step explanation:

step 1

Find the circumference of the road roller

The circumference of a circle is equal to

$C=2\pi r$

we have

$r=77\ cm$

Convert to meters

$r=77\ cm=77/100=0.77\ m$

assume

$\pi =3.14$

substitute

$C=2(3.14)(0.77)$

$C=4.8356\ m$

step 2

Calculate the number of revolutions that the roller will take to cover an area of 96.8 meter square

Remember that

The circumference of complete circle subtends one revolution

The circumference multiplied by the wide of road roller is equal to the area cover for the roller in one revolution

$wide=80\ cm$ ----> $wide=0.80\ m$

$4.8356(0.80)=3.86848\ m^2$

so

using proportion

Find out the number of revolutions for an area of 96.8 meter square

$\frac{3.86848}{1}\ \frac{m^2}{rev}=\frac{96.8}{x}\ \frac{m^2}{rev} \\\\x=96.8/3.86848\\\\x=25\ rev$