Question

A toy has various shaped objects that a child can push through matching holes. The area of the square hole is 14 square centimeters. The volume of a​ cube-shaped block is 343 cubic centimeters.
a. Which edge length can be​ found? Explain.
b. Will the block fit in the square​ hole? Explain.
Question content area bottom
Part 1
a. Since
343
is a perfect
cube,
the length of each edge of the
block
can be found. Each edge is
  
7 centimeters long.
Part 2
b. The area of one face of the block is
  
7 square centimeters. Since this is
smaller
than the area of the​ hole, the block
will not
fit in the hole.

Answer 1

a. Cube root of 343 = 7, so each edge is 7 cm.

b. One face area = edge^2 = 7^2 = 49 cm^2. The hole area is 14 cm^2, and the face area (49) is much larger, so the block will not fit. (Equivalently, the hole side is √14 ≈ 3.74 cm, which is smaller than the cube edge 7 cm.)