Question
describe the formula for finding the area of a circle multiply pi by the length of
A. a diameter
B. a tangent
C. a radius squared
D. an inscribed angle
A. a diameter
B. a tangent
C. a radius squared
D. an inscribed angle
Answers
Answered by
GPT-4o mini
The formula for finding the area of a circle is given by:
\[ \text{Area} = \pi r^2 \]
where \( r \) is the radius of the circle.
Now, looking at your options:
A. **A diameter**: The diameter \( (d) \) is twice the radius (\( d = 2r \)). Therefore, if you were to use the diameter to find the area, you would first need to divide it by 2 to get the radius, and then use the area formula. So, simply multiplying \(\pi\) by the length of the diameter does not yield the area directly.
B. **A tangent**: A tangent to a circle is a line that touches the circle at exactly one point and doesn't have a relation to the area of the circle. Thus, \(\pi\) multiplied by the length of a tangent does not provide the area of the circle.
C. **A radius squared**: If you take the radius squared and multiply it by \(\pi\), you get the correct formula for the area of the circle. This corresponds exactly to the formula \( \text{Area} = \pi r^2 \).
D. **An inscribed angle**: An inscribed angle is an angle formed by two chords in a circle which share an endpoint. It does not directly relate to the area of the circle, so multiplying \(\pi\) by the length of an inscribed angle does not yield the area.
Therefore, the correct choice from your options for finding the area of a circle when multiplying \(\pi\) is:
**C. a radius squared**.
\[ \text{Area} = \pi r^2 \]
where \( r \) is the radius of the circle.
Now, looking at your options:
A. **A diameter**: The diameter \( (d) \) is twice the radius (\( d = 2r \)). Therefore, if you were to use the diameter to find the area, you would first need to divide it by 2 to get the radius, and then use the area formula. So, simply multiplying \(\pi\) by the length of the diameter does not yield the area directly.
B. **A tangent**: A tangent to a circle is a line that touches the circle at exactly one point and doesn't have a relation to the area of the circle. Thus, \(\pi\) multiplied by the length of a tangent does not provide the area of the circle.
C. **A radius squared**: If you take the radius squared and multiply it by \(\pi\), you get the correct formula for the area of the circle. This corresponds exactly to the formula \( \text{Area} = \pi r^2 \).
D. **An inscribed angle**: An inscribed angle is an angle formed by two chords in a circle which share an endpoint. It does not directly relate to the area of the circle, so multiplying \(\pi\) by the length of an inscribed angle does not yield the area.
Therefore, the correct choice from your options for finding the area of a circle when multiplying \(\pi\) is:
**C. a radius squared**.