The correct answer is option 3, which states that the area of the sector is 75 cm².

To understand why this is the correct answer, we need to recall the formulas related to the area of a sector. The area of a sector is calculated using the formula A = ([REPLACEMENT]/360)πr², where A is the area, [REPLACEMENT] is the central angle in degrees, π is a constant (approximately equal to 3.14), and r is the radius of the circle.

In this question, the radius of the circle is given as 10 cm and the arc length is given as 15 cm. The arc length is a portion of the circumference of the circle which corresponds to the central angle of the sector. We can calculate the central angle, [REPLACEMENT], using the formula [REPLACEMENT] = (arc length/circumference) × 360.

Substituting the given values, [REPLACEMENT] = (15/2πr) × 360 = (15/2π10) × 360 = 27 degrees.

Now we can use the formula for the area of the sector, A = ([REPLACEMENT]/360)πr², to calculate the area. Substituting the values, A = (27/