Explanation:
To calculate the volume of the bucket, we can use the formula for the volume of a frustum (a truncated cone):
V = (1/3)πh (r₁² + r₂² + r₁r₂)
where h is the height of the frustum, r₁ and r₂ are the radii of the top and bottom circles respectively.
In this case, the height (h) of the frustum is 4 cm, the top radius (r₁) is half of the top diameter, which is 12 cm / 2 = 6 cm, and the bottom radius (r₂) is half of the bottom diameter, which is 8 cm / 2 = 4 cm.
Substituting these values into the formula, we get:
V = (1/3)π(4) (6² + 4² + 6*4)
= (1/3)π(4) (36 + 16 + 24)
= (1/3)π(4) (76)
= (4/3)π(38)
= 50.265 cm³ (approx)
Therefore, the volume of the bucket is approximately 50.265 cm³.