This question was asked in 2011 cbse board exam. Question from RS Aggarwal book chapter volume and surface area of solid, page number 823, exercise 17C, problem number 12
Deepak BoraNewbie
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
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solution
given data
Height, h=15 cm
Radius of the upper end, R=14 cm
Radius of lower end=r,
Volume of the bucket=5390 cm³
Volume of the bucket = [1/3] π h [R²+r²+rR] = 5390
[1/3]×[22/7]×15×[14²+r²+[14r]] = 5390
196+r²+14r = 5390×7110
196+r²+14r = 343
r²+14r-147=0
r²+21r-7r-147=0
rr+21-7r+21=0
r+21r-7=0
r+21=0 or r-7=0
r=-21 or r=7
r cannot be negative
∴ r=7 cm
∴ the value of r is 7 cm.