Pregunta
(a)
(b)
The area of a quadrant of a circle whos
circumference is 22 cm is
(b)
The area of a quadrant of a circle whos
circumference is 22 cm is
Ask by May Gonzalez. in India
Jan 31,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The area of the quadrant is
cm², which is approximately 9.63 cm².
Solución
To find the area of a quadrant of a circle with a circumference of 22 cm, follow these steps:
Step 1: Calculate the Radius
The formula for the circumference
of a circle is:
Given
cm, solve for
:
Step 2: Calculate the Area of the Full Circle
The area
of a full circle is:
Substitute
:
Step 3: Calculate the Area of the Quadrant
A quadrant is one-fourth of a circle. Therefore:
Step 4: Numerical Approximation (Optional)
If you prefer a numerical value:
Final Answer:
The area of the quadrant is cm², which is approximately 9.63 cm².
The area of the quadrant is
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The Deep Dive
To find the area of a quadrant of a circle when given its circumference, we first need to determine the radius. The circumference
of a circle is given by the formula
. Given that the circumference is 22 cm, we can rearrange the formula to find the radius:
Now, the area
of a full circle is
. For our circle:
Since we need the area of a quadrant (which is a quarter of the full circle):
So, the area of the quadrant of the circle is approximately
.
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