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