10 cm long cylindricalfrustum of a cone. If thdiameter of the cylindr1

1.	10 cm long cylindricalfrustum of a cone. If thdiameter of the cylindr12.CBSE 2012The radii of the circular ends of a bucket of height 15 cm are 14 cm andr em (r< 14). If the volume of bucket is 5390 cm3, find the value of r
Answer» Volume of the bucket=1/3πh(R²+r²+Rr) =5390=1/322/715(196+r²+14r) =5390=22/75(196+r²+14r) =53907/110=196+r²+14r =49*7=196+r²+14r =343=196+r²+14r =0=196-343+r²+14r =0=r²+14r-147 =r²+21r-7r-147=0 =r(r+21)-7(r+21)=0 =(r-7)(r+21)=0 r=7 or -21(rejected) hence r=7

10 cm long cylindricalfrustum of a cone. If thdiameter of the cylindr12.CBSE 2012The radii of the circular ends of a bucket of height 15 cm are 14 cm andr em (r< 14). If the volume of bucket is 5390 cm3, find the value of r

Answer»

Volume of the bucket=1/3πh(R²+r²+Rr)

=5390=1/3*22/7*15(196+r²+14r)

=5390=22/7*5(196+r²+14r)

=5390*7/110=196+r²+14r

=49*7=196+r²+14r

=343=196+r²+14r

=0=196-343+r²+14r

=0=r²+14r-147

=r²+21r-7r-147=0

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

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

r=7 or -21(rejected)

hence r=7