Question

The ratio of the surface area of two spheres is 3:2. The volume of the larger sphere is 2,916 in3. What is the volume of the smaller sphere?


5,357 in3
1,587 in3
864 in3
1,296 in3

Answer 1

\(\large {
\cfrac{volume_{large}}{volume_{small}}=\cfrac{(side_{large})^3}{(side_{small})^3}\implies \cfrac{volume_{large}}{volume_{small}}=\left(\cfrac{(side_{large})}{(side_{small})}\right)^{\color{brown}{ 3}}
\\ \quad \\
\sqrt[{\color{brown}{ 3}}]{\cfrac{volume_{large}}{volume_{small}}}=\cfrac{(side_{large})}{(side_{small})}\qquad thus
\\ \quad \\
\cfrac{2,916}{x}=\left(\cfrac{3}{2}\right)^3\implies \sqrt[3]{\cfrac{2,916}{x}}=\cfrac{3}{2}
}\)

solve for "x"