Given: volume of bucket = 5390 cm3

Radius of upper circular end = R = 14 cm

Radius of lower circular end = r cm & r is less than 14

Height of bucket = h = 15

Volume of bucket = volume of frustum of cone

5390 × 7 = 22 × 5 × (196 + r2 + 14r)

37730/110 = 196 + r2 + 14r

343 = 196 + r2 + 14r

r2 + 14r-147 = 0

r2 + 21r-7r-147 = 0

r(r + 21)-7(r + 21) = 0

(r-7)(r + 21) = 0

r = 7 or r = -21

Since we require r<14 r = 7 cm

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