Question

question 8 of 9 identify the circumference of the circle with a radius of 8.1 inches, both in terms of π and to the nearest tenth. use 3.14 for π. 16.2π in.; 50.9 in. 15.8π in.; 49.6 in. 16.2π in.; 49.6 in. 15.8π in.; 50.9 in.

Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius of the circle.

Step2: Calculate the circumference in terms of \( \pi \)

Given that the radius \( r = 8.1 \) inches. Substitute \( r = 8.1 \) into the formula \( C = 2\pi r \):
\( C = 2\pi\times8.1 = 16.2\pi \) inches.

Step3: Calculate the circumference using \( \pi = 3.14 \)

Substitute \( \pi = 3.14 \) and \( r = 8.1 \) into the formula \( C = 2\pi r \):
\( C = 2\times3.14\times8.1 \)
First, calculate \( 2\times3.14 = 6.28 \)
Then, calculate \( 6.28\times8.1 \):
\( 6.28\times8.1 = 6.28\times(8 + 0.1)=6.28\times8+6.28\times0.1 = 50.24+0.628 = 50.868 \)
Rounding \( 50.868 \) to the nearest tenth gives \( 50.9 \)? Wait, no, wait. Wait, 50.868 to the nearest tenth: the hundredth digit is 6, which is greater than 5, so we round up the tenth digit. The tenth digit is 8, so \( 8 + 1 = 9 \), so it is 50.9? Wait, but let's check again. Wait, 2*3.14*8.1: 2*8.1=16.2, 16.2*3.14. Let's calculate 16*3.14 = 50.24, 0.2*3.14 = 0.628, so total is 50.24 + 0.628 = 50.868. Rounding to the nearest tenth: look at the hundredth place, which is 6. So 50.868 rounded to the nearest tenth is 50.9? But wait, the options have 49.6 or 50.9. Wait, maybe I made a mistake. Wait, no, wait: 2*3.14*8.1. Let's recalculate: 8.1*2=16.2; 16.2*3.14. Let's do 16*3.14=50.24, 0.2*3.14=0.628, so 50.24+0.628=50.868. So to the nearest tenth, 50.868 is 50.9? But wait, the options: the third option is 16.2π in.; 49.6 in. Wait, maybe I miscalculated. Wait, no, wait, maybe the radius is 7.9? No, the radius is 8.1. Wait, maybe the options are wrong? Wait, no, wait, let's check the options again. Wait, the first option is 16.2π in.; 50.9 in. The third option is 16.2π in.; 49.6 in. Wait, my calculation gives 50.868, which is approximately 50.9. But let's check the formula again. Wait, circumference formula is \( C = 2\pi r \), so with \( r = 8.1 \), \( C = 2\pi*8.1 = 16.2\pi \). Then with \( \pi = 3.14 \), \( C = 16.2*3.14 = 50.868 \approx 50.9 \). So the first option is 16.2π in.; 50.9 in. But wait, let's check the options again. Wait, the first option is 16.2π in.; 50.9 in. The third option is 16.2π in.; 49.6 in. So where is the mistake? Wait, maybe I made a mistake in the radius. Wait, the problem says radius of 8.1 inches. Wait, 2*3.14*8.1: 2*8.1=16.2, 16.2*3.14. Let's calculate 16.2*3.14:

16.2 * 3.14:

Multiply 162 * 314 (ignoring decimals) and then adjust the decimal places.

162 * 314:

162 * 300 = 48600

162 * 14 = 2268

Total = 48600 + 2268 = 50868

Now, 16.2 has one decimal place, 3.14 has two decimal places, so total decimal places is 1 + 2 = 3. So 50868 / 1000 = 50.868, which is 50.868. Rounding to the nearest tenth: 50.9 (since the hundredth digit is 6, which is more than 5, so we round up the tenth digit from 8 to 9). But wait, the first option is 16.2π in.; 50.9 in. But let's check the options again. Wait, maybe I made a mistake in the formula? No, circumference is \( 2\pi r \), so that's correct. So the circumference in terms of π is 16.2π, and using π=3.14, it's 50.868, which rounds to 50.9. But wait, the first option is 16.2π in.; 50.9 in. But let's check the options again. Wait, the first option is "16.2π in.; 50.9 in." But when I calculated 2*3.14*8.1, I got 50.868, which is 50.9 when rounded to the nearest tenth. So the correct option should be the first one? Wait, but let's check the options again. Wait, the third option is 16.2π in.; 49.6 in. That must be a mistake. Wait, maybe the radius is 7.9? No, the problem says 8.1. Wait, maybe I miscalculated 2*3.14*8.1. Let's do it again: 8.1*2=16.2; 16.2*3.14. 3*16.2=48.6, 0.14*16.2=2.268, so 48.6 + 2.268=50.868. Yes, that's correct. So 50.868 rounded to the nearest tenth is 50.9. So the first option is 16.2π in.; 50.9 in. So that's the correct answer.

Wait, but wait, the options:

First option: 16.2π in.; 50.9 in.

Second: 15.8π in.; 49.6 in.

Third: 16.2π in.; 49.6 in.

Fourth: 15.8π in.; 50.9 in.

So according to our calculation, the circumference in terms of π is 16.2π, and the numerical value is 50.868 ≈ 50.9. So the first option is correct.

Answer:

A. 16.2π in.; 50.9 in.