Question

Lin and his sister use blocks to build cubes. Lin's cube measured 5 in on each side. His sister's cube measured 15 inches on each side. How many times larger is the volume of Lin's sister's cube?How many times larger is the surface area of Lin's sister's cube?

Answer 1

Volume

The formula to find the volume of a cube is:

`\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}`

Then, we have:

• The volume of Lin's cube is 125 cubic inches.

`\begin{gathered} s=5in \\ V=s^3 \\ V=(5in)^3 \\ V=5^3in^3 \\ V=5\cdot5\cdot5in^3 \\ V=125in^3 \end{gathered}`

• The volume of Lin's sister cube is 3375 cubic inches.

`\begin{gathered} s=15in \\ V=s^3 \\ V=(15in)^3 \\ V=15^3in^3 \\ V=15\cdot15\cdot15in^3 \\ V=3375in^3 \end{gathered}`

Now, we divide both volumes:

`(3375in^3)/(125in^3)=(3375)/(125)=27`

Therefore, the volume of Lin's sister cube is 27 times larger than the volume of Lin's cube.

Surface area

The formula to find the surface area of a cube is:

`\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}`

Then, we have:

• The surface area of Lin's cube is 150 square inches.

`\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}`

• The surface area of Lin's sister cube is

`\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}`

Now, we divide both surfaces areas:

`(1350in^2)/(150in^2)=(1350)/(150)=9`

Therefore, the surface area of Lin's sister cube is 9 times larger than the surface area of Lin's cube.