The diameter of a circle is 13 cm. Find its area to the nearest tenth.
The Correct Answer and Explanation is :
To find the area of a circle, we use the formula:
[
A = \pi r^2
]
where:
- ( A ) is the area,
- ( r ) is the radius of the circle,
- ( \pi ) (pi) is approximately ( 3.1416 ).
Step 1: Find the radius
The radius of a circle is half of its diameter. Since the diameter of the circle is given as 13 cm, we can calculate the radius:
[
r = \frac{\text{diameter}}{2} = \frac{13}{2} = 6.5 \, \text{cm}
]
Step 2: Apply the formula for the area
Now that we know the radius is 6.5 cm, we can substitute this value into the area formula:
[
A = \pi r^2 = 3.1416 \times (6.5)^2
]
First, square the radius:
[
6.5^2 = 42.25
]
Now multiply by ( \pi ):
[
A = 3.1416 \times 42.25 = 132.7326
]
Step 3: Round the answer
The area, to the nearest tenth, is 132.7 cm².
Final Answer:
The area of the circle is approximately 132.7 cm².
Explanation
The area of a circle is directly related to the square of its radius. Since the diameter of the circle is 13 cm, we first calculate the radius by dividing the diameter by 2, yielding a radius of 6.5 cm. Squaring the radius gives 42.25, which is then multiplied by ( \pi ) (approximately 3.1416) to get the area. The final step is rounding the result to the nearest tenth to match the desired precision. This gives the area as 132.7 cm².
This approach is based on the well-known formula for the area of a circle, and it helps to remember that the diameter is twice the radius, which simplifies the calculation process.