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A roller of diameter 70 cm and length 2m is rolling on the ground What is the area covered by the roller in 50 revolutions?
Answer
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Hint: Roller is in a shape of Cylinder. Its one turn of rolling will cover the ground equal to its curved surface area. Thus in this way we can find the area of ground in 50 such revolutions of the roller.
Complete step-by-step answer:
This type of question is very common in mensuration. First we have to calculate the curved surface area of the cylinder.
Formula for curved surface area of cylinder is:
$A = 2\pi rh$
Where r is the radius and h is the height of the cylinder.
So, r = $\dfrac{{70}}{2}$=35 cm= 0.35 m (As radius is half of the diameter.)
And h= 2 m
Now, we will substitute the values of r and h in the above formula. Then we will get,
$
A = 2 \times \dfrac{{22}}{7} \times 0.35 \times 2 \\
\Rightarrow A = 4.4 \\
$
Thus the area covered by the roller in one revolution will be 4.4 square meters.
Now, to find the total area covered by roller in 50 revolutions, we need to multiply the area covered in one revolution by 50.
Therefore,
$
50 \times 4.4 \\
\Rightarrow 220 \\
$
Area covered in 50 revolutions will be 220 square meters.
Note: Surface area of any solid substance is the measure of the total area occupied by the surface of the substance. Volume of a substance is the space that a substance contains.
Complete step-by-step answer:
This type of question is very common in mensuration. First we have to calculate the curved surface area of the cylinder.
Formula for curved surface area of cylinder is:
$A = 2\pi rh$
Where r is the radius and h is the height of the cylinder.
So, r = $\dfrac{{70}}{2}$=35 cm= 0.35 m (As radius is half of the diameter.)
And h= 2 m
Now, we will substitute the values of r and h in the above formula. Then we will get,
$
A = 2 \times \dfrac{{22}}{7} \times 0.35 \times 2 \\
\Rightarrow A = 4.4 \\
$
Thus the area covered by the roller in one revolution will be 4.4 square meters.
Now, to find the total area covered by roller in 50 revolutions, we need to multiply the area covered in one revolution by 50.
Therefore,
$
50 \times 4.4 \\
\Rightarrow 220 \\
$
Area covered in 50 revolutions will be 220 square meters.
Note: Surface area of any solid substance is the measure of the total area occupied by the surface of the substance. Volume of a substance is the space that a substance contains.
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