In a circle with a diameter of 32, the area of a sector with angle t is what?

Circles are very important and interesting shapes that form an integral part of geometry in mathematics. Now, let's solve a question related to the concepts of circles.

Answer: In a circle with a diameter of 32, the area of a sector with angle t is 2.24t.

Let's understand the solution in detail.

Explanation:

The area of a circle is given by πr², where r is the radius.

And, the area of a sector of a circle with angle t is given by πr² × t / 360

Also, in the given circle, diameter = 32.

Hence, the radius = 16.

Hence, the area of the sector of this circle with angle t is A = t / 360 × π(16)².

Now, using π = 3.142, we get A = 2.24t.

Now, we can put any value of t to get the specific area of a given sector with a particular measure of the angle.

For example, if t = 90 degrees, then Area A = 201.6.

Hence, in a circle with a diameter of 32, the area of a sector with angle t is 2.24t.