Question

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

Answer 1

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

Answer 2

Here is your solutions

Given :-
Thee radii of the circular ends of a bucket of

Height = 15cm

r = 14cm

volume of bucket = 5390cm3

To find the value of r :-

we know that

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

=>196-343+r²+14r=0

=>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

hence
radius of bucket =7cm

hope it helps you