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Question
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 bucket is 5390 cm3, then find the value of r.
Solution
We have,
Height, h = 15 cm,
Radius of the upper end, R = 14 cm
Radius of lower end = r,
As,
Volume of the bucket = 5390 cm3
`rArr 1/3 pi"h"("R"^2 + r^2 + Rr)=5390 "cm"^3`
`rArr 1/3 xx 22/7xx15xx(14^2+r^2+14r) = 5390`
`= 110/7xx(196+r^2+14r)=5390`
`rArr 196 + r^2+14r=(5390xx7)/110`
`rArr 196 + r^2 + 14r = 343`
`rArr r^2 + 14"r"- 147 = 0`
`rArr r^2 + 21r - 7r-147 = 0`
⇒ r (r + 21)-7(r+21)=0
⇒ (r+21)(r-7)=0
⇒ r + 21 = 0 or r=7
As, connot be negative
∴ r = 7 cm
So the value of r id 7
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