The formula to find the volume of a cube is:
[tex]\begin{gathered} V=s^3 \\ \text{ Wher V is the volume and} \\ s\text{ is the length of a side of the cube} \end{gathered}[/tex]Then, we have:
• The volume of Lin's cube is 125 cubic inches.
[tex]\begin{gathered} s=5in \\ V=s^3 \\ V=(5in)^3 \\ V=5^3in^3 \\ V=5\cdot5\cdot5in^3 \\ V=125in^3 \end{gathered}[/tex]• The volume of Lin's sister cube is 3375 cubic inches.
[tex]\begin{gathered} s=15in \\ V=s^3 \\ V=(15in)^3 \\ V=15^3in^3 \\ V=15\cdot15\cdot15in^3 \\ V=3375in^3 \end{gathered}[/tex]Now, we divide both volumes:
[tex]\frac{3375in^3}{125in^3}=\frac{3375}{125}=27[/tex]Therefore, the volume of Lin's sister cube is 27 times larger than the volume of Lin's cube.
The formula to find the surface area of a cube is:
[tex]\begin{gathered} SA=6s^2 \\ \text{ Where SA is the surface area and } \\ s\text{ is the length of a side of the cube} \end{gathered}[/tex]Then, we have:
• The surface area of Lin's cube is 150 square inches.
[tex]\begin{gathered} s=5in \\ SA=6s^2 \\ SA=6(5in)^2 \\ SA=6(5)^2in^2 \\ SA=6\cdot5\cdot5in^2 \\ SA=150in^2 \end{gathered}[/tex]• The surface area of Lin's sister cube is
[tex]\begin{gathered} s=15in \\ SA=6s^2 \\ SA=6(15in)^2 \\ SA=6(15)^2in^2 \\ SA=6\cdot15\cdot15in^2 \\ SA=1350in^2 \end{gathered}[/tex]Now, we divide both surfaces areas:
[tex]\frac{1350in^2}{150in^2}=\frac{1350}{150}=9[/tex]Therefore, the surface area of Lin's sister cube is 9 times larger than the surface area of Lin's cube.
