Question

Find area of a circle with radius $ 5\;mm $ , rounded to the nearest tenth?

Answer 1

Hint: The given question requires us to find the area of a circle with radius of $ 5\;mm $ and then rounding it off to the nearest tenth. The area of a circle can be calculated by using the formula for the same given the radius of the circle as $ 5\;mm $ . Then we have to round off the area of the circle to nearest tenth. Rounding off of numbers has certain rules that have to be followed.

Complete step-by-step answer:
Area of circle $ = $ $ \pi {r^2} $ , where r $ = $ radius of circle.
Taking the value of $ \pi $ as $ \dfrac{{22}}{7} $ , we get,
Area of circle $ = $ $ \dfrac{{22}}{7}{\left( {5mm} \right)^2} $
Area of circle $ = $ $ \dfrac{{22}}{7} \times 25{\text{ }}m{m^2} $
Area of circle $ = $ $ \dfrac{{550}}{7}{\text{ }}m{m^2} $
Area of circle $ = $ $ 78.5714...{\text{ }}m{m^2} $
So, the area of the circle with radius as $ 5\;mm $ is $ 78.5714...{\text{ }}m{m^2} $ .
Now the area of the circle has to be rounded off to nearest tenth, we get
Area of circle $ = $ $ 78.6{\text{ }}m{m^2} $
So, the area of a circle with radius $ 5\;mm $ , rounded to the nearest tenth is $ 78.6{\text{ }}m{m^2} $ .
So, the correct answer is “ $ 78.6{\text{ }}m{m^2} $ . ”.

Note: The given problem could also be solved by first changing the units of length from millimetres to centimetres or metres and then evaluating the area and rounding it off to the nearest tenth. But, the answer that we would obtain by first converting the units, calculating the area and then rounding it off to nearest tenths would be much less accurate than the answer as changing the unit of length to a bigger unit increases the percentage of error in rounding off and calculations