Question

question 2 of 9
find the area of a circle with diameter 38 mm, both in terms of π and to the nearest tenth. use 3.14 for π.
a = 76π mm² ≈ 238.6 mm²
a = 361π mm² ≈ 1133.5 mm²
a = 38π mm² ≈ 119.3 mm²
a = 1,444π mm² ≈ 4534.2 mm²

Explanation:

Step1: Find the radius

The diameter \( d = 38 \) mm, so the radius \( r=\frac{d}{2}=\frac{38}{2} = 19 \) mm.

Step2: Calculate area in terms of \( \pi \)

The formula for the area of a circle is \( A=\pi r^{2} \). Substituting \( r = 19 \), we get \( A=\pi\times19^{2}=\pi\times361 = 361\pi \) \( \text{mm}^2 \).

Step3: Calculate the numerical value

Using \( \pi = 3.14 \), \( A=361\times3.14 = 1133.54 \). Rounding to the nearest tenth, we look at the hundredth place which is 4. Since \( 4<5 \), we round down. So \( A\approx1133.5 \) \( \text{mm}^2 \).

Answer:

B. \( A = 361\pi \text{ mm}^2 \approx 1133.5 \text{ mm}^2 \)