Problema Solution
The rectangular prism shown has a height of 2 1/2 inches, a length of 1 1/2 inches, and a width of 1/2 inch.
Part A: Suppose you have cubes that are 1 1/2 inch on each side. How many of these cubes would it take to fill a cube that is 1 inch high, 1 inch long and 1 inch wide?
Part B: Use your answer to Part A to find the volume of one of the 1/2 inch cubes.
Part C: How many 1/2 inch cubes would it take to fill the prism?
Part D: Use your answers to Part B and C to find the volume of the prism.
Part E: Multiply the height, length and width of the prism.
Compare this product to your answer to Part D
Answer provided by our tutors
Solution (A):
N = 1^3 /(1/2)^3 = 8
So 8 cubes are needed
Solution (B):
V = (1/2)^3 = 1/8 cubic inches
Solution (C):
N = 2.5*1.5*0.5/(0.5)^3 = 15
So 15 cubes are needed
Solution(D)
V(prism) = 15*(1/8) = 1 7/8 cubic inches
Solution(E):
V = 2.5*1.5*0.5 = 1 7/8 cubic inches, same with (D)