According to the question,
The bucket is in the form of frustum of a cone.
We know that,
Volume of frustum of a cone = 1/3 πh(r12 + r22 + r1r2), where, h = height, r1 and r2 are the radii(r1 > r2)
For bucket,
Volume of bucket = 28.490 L
1 L = 1000 cm3
Volume of bucket = 28490 cm3
Radius of top, r1 = 28 cm
Radius of bottom, r2 = 21 cm
Let the height = h.
Substituting these values in the equation to find the volume of bucket,
We have.
Volume of bucket = 1/3 πh[282 + 212 + 28(21)]
28490 = 1/3 × 22/7 × h (784 + 441 + 588) = 22/7 × h × 1813
⇒ h = (28490 × 21) / (22 × 1813)
⇒ h = 15