Question

if a circle has a diameter of 20mm then what is the area of this circle if you use ( pi = 3.142 )?

Explanation:

Step1: Find the radius

The diameter \( d = 20 \, \text{mm} \), so the radius \( r=\frac{d}{2}=\frac{20}{2} = 10 \, \text{mm} \).

Step2: Calculate the area

The formula for the area of a circle is \( A=\pi r^{2} \). Substitute \( \pi = 3.142 \) and \( r = 10 \, \text{mm} \):
\( A=3.142\times(10)^{2}=3.142\times100 = 314.2 \, \text{mm}^2 \)? Wait, wait, wait, let's check the options. Wait, maybe I miscalculated? Wait, no, wait the options: one of them is 314.2 mm²? Wait, the original problem's options: let's re - check. Wait, the diameter is 20 mm, radius is 10 mm. Area \( A=\pi r^{2}=3.142\times10^{2}=3.142\times100 = 314.2 \, \text{mm}^2 \). But wait, maybe the options have a typo? Wait, no, maybe I made a mistake. Wait, no, the formula is correct. Wait, the options: let's see the options again. Wait, the first option is 3142 mm², second 100, third 400, fourth 31.42 m² (wrong unit), fifth 314.2 mm². Wait, maybe the correct answer is 314.2 mm²? Wait, but let's recalculate. \( r = 20\div2=10 \), \( A = 3.142\times10\times10=314.2 \, \text{mm}^2 \). So the correct option should be the one with 314.2 mm².

Answer:

The option with "314.2 mm²" (assuming the last option is 314.2 mm², as per the calculation \( A=\pi r^{2}=3.142\times(10)^{2}=314.2 \, \text{mm}^2 \) where \( r = \frac{20}{2}=10 \, \text{mm} \))