Math  /  Geometry

QuestionA circle with a diameter of 16 yd is shown. Answer the parts below. Make sure you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact circumference of the circle. Write your answer in terms of π\pi. Exact circumference: \square (b) Using the ALEKS calculator, approximate the circumference of the circle.
To do the approximation, use the π\pi button on the calculator, and round your answer to the nearest hundredth.
Approximate circumference: \square

Studdy Solution

STEP 1

1. The diameter of the circle is given as 16 yards.
2. The formula for the circumference of a circle is C=π×d C = \pi \times d , where d d is the diameter.
3. For approximation, use the value of π\pi from the calculator.

STEP 2

1. Calculate the exact circumference in terms of π\pi.
2. Approximate the circumference using a calculator.

STEP 3

Identify the formula for the circumference of a circle. The formula is:
C=π×d C = \pi \times d

STEP 4

Substitute the given diameter into the formula. Here, d=16 d = 16 yards. Thus, the exact circumference is:
C=π×16 C = \pi \times 16

STEP 5

Simplify the expression to find the exact circumference in terms of π\pi:
C=16π C = 16\pi
Exact circumference: 16π \boxed{16\pi}

STEP 6

Use the calculator to approximate the value of the circumference. Enter 16×π 16 \times \pi using the π\pi button.

STEP 7

Round the result to the nearest hundredth. Assuming π3.14159265\pi \approx 3.14159265, calculate:
16×3.1415926550.2654824 16 \times 3.14159265 \approx 50.2654824
Rounded to the nearest hundredth, the approximate circumference is:
50.27 \boxed{50.27}
The exact circumference of the circle is 16π 16\pi yards, and the approximate circumference is 50.27 50.27 yards.

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