Answer:
The side length of the blocks is 5 inches
the total surface area of the 27 blocks = 27 x 150 = 4050 square inches
This is 3 times the surface area of the box.
Step-by-step explanation:
From the information given,
the cube shaped box with side length of 15 inches contains 27 identical cube-shaped blocks. Recall, the length of each side of a cube is equal. We would calculate the volume of the cube shaped box. The formula for calculating the volume of a cube is
Volume = s^3
Volume of cube shaped box = 15^3 = 3375
Thus,
Volume of 27 identical cube-shaped blocks = 3375
Volume of one identical cube-shaped block = 3375/27 = 125 in^2
We would find the side length of one identical cube-shaped block
Thus,
125 = s^3
Taking the cube root of both sides,
s = cube root of 125
s = 5
The side length of the blocks is 5 inches
The formula for calculating the surface area of a cube is expressed as
surface area = 6a^2
Surface area of larger cube = 6 x 15^2 = 1350
surface area of each small block = 6 x 5^2 = 150
the total surface area of the 27 blocks = 27 x 150 = 4050 square inches
Ratio of surface area of the 27 blocks to the original box = 4050/1350 = 3
This is 3 times the surface area of the box.