Final answer:
To find the area of the cup's base in the cupcake tray, we use the circle area formula with the radius half of the given diameter. The diameter is 36 mm, so the radius is 18 mm, or 0.018 m. The calculated area is then approximately 1018 mm² or 10.18 cm².
Step-by-step explanation:
To calculate the area of the cup which has a circular cross-section, we will use the area formula for a circle, which is π×r², where π is a constant approximately equal to 3.14159, and r is the radius of the circle. The diameter of the cup is given as 36 millimeters, so the radius, which is half of the diameter, is 36 mm ÷ 2, or 18 mm. Convert this to meters by dividing by 1000, giving us 0.018 meters. Plugging the radius into the area formula gives us π×(0.018 m)².
Calculating this we get: π×(0.018 m)·(0.018 m) = π×(0.000324 m²) ≈ 0.001018 m², which we can convert back to square millimeters by multiplying by 1,000,000 (since 1 m² = 1,000,000 mm²), resulting in an area of approximately 1018 mm². However, the original question asks for the area in a more standard unit of measure, so we typically report it in square centimeters. To convert square millimeters to square centimeters, divide by 100 (since 1 cm² = 100 mm²), which gives an area of 10.18 cm².