Question

6. the ratio of the volumes of the two spheres is 27:343 and the sum of their radii is 10. find the radius of the smaller sphere.

Answer 1

let V1 and V2 be the volumes.
Then\[\frac{ V1 }{ V2 }=\frac{ 27 }{ 343 }=\frac{\frac{ 4 }{ 3 } \pi \left( R1 \right)^3 }{ \frac{ 4 }{ 3 }\pi \left( R2 \right)^3 }\]
Where R1 and R2 arethe radii of the two spheres.
\[\left( \frac{ R1 }{ R2 } \right)^3=\frac{ 27 }{343 }=\left( \frac{ 3 }{ 7 } \right)^3\]
\[\frac{ R1 }{R2 }=\frac{ 3 }{7 },R1=\frac{ 3 }{ 7 }R2\]
Also R1+R2=10
\[\frac{ 3 }{7 }R2+R2=10,3R2+7R2=10*7,10R2=70,R2=70/10=7\]
find R1