Question

Select the correct answer from each drop-down menu. A cube shaped box has a side length of 15 inches and contains 27 identical cube shaped blocks. What is the surface area of all 27 blocks compared to the surface area of the box? The side length of the blocks is (3,4 or 5) inches, so the total surface area of the 27 blocks is (150, 4,050 or 1350) square inches. This is (5 times, 3 times, one third or one-fifth) the surface area of the box.I need someone to answer the answers in the ( )

Answer 1

The formula to calculate the surface area of a cube is given by

$SA=6b^2$

where

b is the long side of the cube

step 1

Find out the surface area of the cube with a side length of 15 inches

$\begin{gathered} SA=6(15)^2 \\ SA=1,350\text{ in}^2 \end{gathered}$

step 2

Find out the surface area of all 27 blocks

Remember that

27=3^3

so

The side length of the blocks is 15/3=5 in

Find out the surface area

$\begin{gathered} SA=27[6(5)^2] \\ SA=4,050\text{ in}^3 \end{gathered}$

Compare both surface areas

4,050/1,350=3

therefore

The total surface area of the 27 blocks is 4,050 square inches. This is 3 times the surface area of the box