We know that the angle of 2.7 radians intercepts an arc of length 46.7 units in a circle. We can use the formula relating the angle in radians, central angle in degrees, and the radius of the circle:
length of arc = (central angle in degrees / 360°) x 2πr
where r is the radius of the circle.
First we need to convert the angle of 2.7 radians to degrees by multiplying by 180°/π, which gives:
angle in degrees = 2.7 x 180°/π ≈ 154.43°
Now we can plug in the known values into the formula:
46.7 = (154.43° / 360°) x 2πr
Simplifying:
46.7 = 0.429 x 2πr
r ≈ 46.7 / (0.429 x 2π) ≈ 17.01 units
Therefore, the radius of the circle to the nearest 10th is 17.0 units.