Topic
The bottom of a milk carton is in the shape of a circle with a radius of 4 cm. Calculate the area of the bottom surface of the milk carton.
a) Is it possible to use a finite number of decimal places to accurately record the area of the bottom of the milk carton? Why?
b) Hoa and Binh respectively give the results of calculating the area of the bottom of the milk carton as \({S_1} = 49.6c{m^2}\) and \({S_2} = 50.24c{m) ^2}\). Which one gives more accurate results?
Solution method – See details
The area of the circle is \(S = \pi {R^2}\) where \(R\) is the radius of the circle.
Compare \({S_1},{S_2}\) and the exact area of the circle. The result that is closer to the correct number is more accurate.
Detailed explanation
The area of the bottom surface of a circular milk carton with radius \(R = 4\)(cm) is \(S = \pi {.4^2} = 16\pi \left( {c{m^2}} \right)\)
a) Since \(\pi = 3.141592653…\) is an irrational number, the area S is also an irrational number, so finite decimals cannot be used to accurately record the area of the bottom of the milk carton.
b) Comparing \({S_1},{S_2}\) and the exact area of the bottom surface, we have: \({S_1} < {S_2} < 50.26548… = 16\pi \) so you Binh for more accurate results
