Final answer:
To obtain a perfect cube, divide 128 by the smallest cube number, which is 8. The area of the field can be calculated using the formula for the area of a circle. Convert the diameter to meters and then use the formula A = π * r^2.
Step-by-step explanation:
To find the smallest number by which 128 must be divided to obtain a perfect cube, we need to find the prime factors of 128. The prime factorization of 128 is 2 * 2 * 2 * 2 * 2 * 2 * 2. To make it a perfect cube, we need to divide it by the smallest cube number possible, which is 2 * 2 * 2 = 8. Therefore, 128 must be divided by 8 to obtain a perfect cube.
To calculate the area of the field, we can use the formula for the area of a circle: A = π * r^2, where r is the radius. Since the diameter is given as 84 cm, the radius is half of that, which is 42 cm. But we need to convert the radius to meters, so we divide by 100 (since there are 100 cm in a meter). So the radius in meters is 0.42 m. Now we can calculate the area using the formula: A = 3.14 * (0.42)^2. The result is the area of the field in square meters.
Learn more about Calculating perfect cubes and area of a circle