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

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# 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.