## Solving Lesson 3 Page 27 Math Workbook 10 – Kite>

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