If the circumference of a circle is 21 inches, what is the diameter? Use 3.14 for and round your answer to the nearest hundredth.
The Correct Answer and Explanation is :
To find the diameter of a circle when given the circumference, we can use the formula for the circumference of a circle:
[
C = \pi \times d
]
where:
- ( C ) is the circumference
- ( \pi ) is approximately 3.14
- ( d ) is the diameter
We are given the circumference ( C = 21 ) inches, and we need to solve for ( d ).
Step 1: Rearrange the formula
We want to solve for ( d ), so we rearrange the formula to isolate ( d ):
[
d = \frac{C}{\pi}
]
Step 2: Substitute the known values
Now, substitute the given value for ( C ) (which is 21 inches) and the approximation for ( \pi ) (3.14):
[
d = \frac{21}{3.14}
]
Step 3: Perform the calculation
Now, divide 21 by 3.14:
[
d = 6.693 \text{ inches}
]
Step 4: Round the answer
Since the problem asks for the diameter to be rounded to the nearest hundredth, we round 6.693 to two decimal places:
[
d \approx 6.69 \text{ inches}
]
Final Answer:
The diameter of the circle is approximately 6.69 inches.
Explanation:
The formula for the circumference of a circle relates the circumference to the diameter by multiplying the diameter by ( \pi ), a mathematical constant approximately equal to 3.14. To solve for the diameter when the circumference is known, we simply rearrange the formula to divide the circumference by ( \pi ). By dividing 21 inches by 3.14, we find the diameter to be about 6.693 inches. After rounding to the nearest hundredth, the diameter is 6.69 inches. This is a common calculation used in geometry to determine the dimensions of a circle when given either the circumference or area.