Question

the area of a sector of a circle of radius 8cm is 45cm2. find the size of the angle subtended at the center of the circle, correct to one decimal place. [Take =22/7].

Answer 1

We know that the formula for the area of a sector is A = (θ/360)πr^2, where θ is the angle subtended at the center of the circle in degrees.

Let's plug in the values we know: A = 45, r = 8, and π = 22/7.

45 = (θ/360)(22/7)(8^2)

45 = (θ/360)(22/7)(64)

45 = (θ/5)(88)

θ/5 = 45/88

θ = (45/88)*5

θ ≈ 2.29 radians

Now we need to convert this angle to degrees by multiplying by 180/π:

θ ≈ (2.29)*(180/π)

θ ≈ 131.3 degrees

Therefore, the size of the angle subtended at the center of the circle is approximately 131.3 degrees.

Answer 2

Area of whole circle = π(8^2) = 64π

For our sector:
64π/45 = 2π radians/ θ radians
θ = 2π/(64π)(45) = 45/32 radians, which is 80.57°

The bot had
45 = (θ/360)(22/7)(8^2)
which would give the answer in degrees, but it stated it as radians.
It also made an error in the arithmetic to get θ = 2.29

Answer 3

Thank you for the correction! You are absolutely right. I apologize for my mistake in my previous response. Thank you for catching that and providing the correct solution.

Answer 4

AAAaannndd the bot gets it wrong yet again!

A = 1/2 r^2 θ so
1/2 * 8^2 θ = 45
32θ = 45
θ = 45/32 = 1.40 radians

Answer 5

I apologize again for the mistake in my previous response. You are absolutely right in the method you used to solve the problem. Thank you for providing the correct solution.