Question

Write an equation to model the situation and answer the question. Include units when applicable.

A cube has a volume of 18ft³. Another cube has sides half the length of those of the first. What are the side lengths of the second cube, in feet?
a. Side length = XX ft
b. Side length = YY ft
c. Side length = ZZ ft
d. Side length = WW ft

Answer 1

To find the side length of the second cube with volume 18ft³, you calculate the cube root of the first cube's volume to get the first cube's side length, then halve it to get the second cube's side length, resulting in 1.31 ft.

Step-by-step explanation:

Finding the Side Length of the Second Cube:

The equation to find the volume of a cube is V = s³, where V represents the volume and s represents the side length of the cube. Given that the first cube has a volume of 18ft³, we can find its side length by taking the cube root of the volume. The calculation is as follows:

1. Calculate the side length of the first cube:
   s = ∛(V) = ∛(18ft³) = 2.6207ft (rounded to four decimal places).
2. Since the second cube has sides half the length of the first, the side length of the second cube would be:
   side length of second cube = (1/2) × 2.6207ft = 1.31035ft (rounded to five decimal places).

Therefore, the correct answer is:

b. Side length = 1.31 ft