The area of a circle is 256π square cm. The length of its longest chord (in cm) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 32.
Let's find the radius of the circle first.
The area of a circle is given by the formula:
Area = πr²
Here, the area is 256π square cm. So,
256π = πr²
Dividing both sides by π, we get:
256 = r²
Taking the square root of both sides:
r = 16 cm
The longest chord of a circle is its diameter. The diameter is twice the radius.
So, the length of the longest chord = 2 × radius = 2 × 16 = 32 cm.
Therefore, the length of the longest chord is 32 cm.