Question

The radii of the circular ends of a bucket of height 15cm are 14cm and r сm (r< 14cm). If the volume of
bucket is 5390cm?. Find the value of r. ​

Answer 1

${\red{\underline{\underline{\bold{Given :-}}}}}$

• Height = 15cm

• r = 14cm

• Volume of bucket = 5390 cm³

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The value of r

${\green{\underline{\underline{\bold{Solution :-}}}}}$

we know that

Volume of the bucket =$\frac{1}{3}πh(R²+r²+Rr)</p><p></p><p>[tex]\implies 5390=\frac {1}{3} × \frac{22}{7}×15(196+r²+14r) \\ \\</p><p></p><p>\implies 5390=\frac{22}{7}×5(196+r²+14r) \\ \\</p><p></p><p>\implies 5390×\frac{7}{110} =196+r²+14r \\ \\</p><p></p><p>\implies 49×7=196+r²+14r \\ \\</p><p></p><p>\implies 343=196+r²+14r \\ \\</p><p></p><p>\implies 196-343+r²+14r=0 \\ \\</p><p></p><p>\implies r²+14r-147=0 \\ \\</p><p></p><p>\implies r²+21r-7r-147=0 \\ \\</p><p></p><p>\impliesr(r+21)-7(r+21)=0 \\ \\</p><p></p><p>\implies (r-7)(r+21)=0 \\ \\</p><p></p><p>\implies r =7 or r = -21$

we will take r= 7 (positive )

Hence

Radius (r) of bucket =7cm