The diagram shows a sector OACB of a circle with centre O - Edexcel - GCSE Maths - Question 23 - 2019 - Paper 3

Now we will use the Pythagorean theorem to find the slant height (l) of the cone:

$$l = \sqrt{r^2 + h^2}$$

Substituting the known values:

$$l = \sqrt{(3.87)^2 + (3.6)^2}$$

Calculating:

$$l = \sqrt{14.9769 + 12.96}$$ $$l = \sqrt{27.9369} ≈ 5.28 ext{ cm}$$

Now we need to find the angle AOB. The arc length (l) of sector OACB can be calculated as being equal to the circumference of the base of the cone:

$$C = 2\pi r ≈ 2\pi (3.87)$$

Calculating:

$$C ≈ 24.34 ext{ cm}$$

Since C forms a circular sector, we can find the angle AOB using the formula:

$$angle = \frac{l}{C} \times 360^{\circ}$$

Substituting our arc length and circumference:

$$angle = \frac{l}{24.34} \times 360^{\circ}$$

Calculating:

$$angle ≈ \frac{5.28}{24.34} \times 360^{\circ}$$

Which results in:

$$angle ≈ 78.0^{\circ}$$

Therefore, the angle AOB is approximately 78.0 degrees.