The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14). If the volume of the bucket is 5390 cm3, find the value of r.
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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