The area of a circular sector is 1790 centimetres squared and the central angle is 1.5 radians. Find the radius of the circle, giving the answer to the nearest centimetre.
So let’s see if we can represent this information on a diagram. We have a circular sector; its area is 1790 centimetres squared and the measure of its central angle is 1.5 radians. And we are required to find the radius of the circle, which I’m going to call 𝑟.
There is a formula for the area of a circular sector. The area is equal to half the radius squared times the measure of the central angle in radians. We are given the area of the circular sector; it’s 1790 centimetres squared, and we are also given the measure of the central angle in radians, 1.5.
Substituting those into the equation we have, we have an equation in terms of 𝑟 alone. Multiplying both sides by two, we get 3580 equals 𝑟 squared times 1.5. Swapping both sides and dividing by 1.5, we get that 𝑟 squared is equal to 2386.6 recurring. And taking square roots on both sides, we get that 𝑟 is equal to 48.85 dot dot dot.
And of course, as the area was given in centimetres squared, this radius length will be in centimetres. And the only thing left to do is to round this answer to the nearest centimetre. So we get that the radius of the circle is 49 centimetres long.