The diameter of a pizza is 30 cm. What is the area (in square cm) of the upper surface of a sector of the pizza whose arc length is 8 cm?

To solve this problem, we need to use the formula for the area of a sector of a circle, which is (θ/2π) * πr², where θ is the central angle of the sector and r is the radius of the circle.

Step 1: Find the radius of the pizza. Since the diameter is given as 30 cm, the radius would be half of that, which is 15 cm.

Step 2: Find the circumference of the pizza. The formula for the circumference of a circle is 2πr. So, the circumference of the pizza is 2π * 15 = 30π cm.

Step 3: Find the central angle θ. The arc length of the sector is given as 8 cm. The central angle is the ratio of the arc length to the circumference, multiplied by 360 degrees. So, θ = (8 / 30π) * 360 = 96/π degrees.

Step 4: Find the area of the sector. Using the formula for the area of a sector, we get (θ/2π) * πr² = (96/π / 2π) * π * 15² = 96/2 * 15²/π = 7200/π cm².

So, the area of the upper surface of the sector of the pizza is 7200/π cm².