Question

a) a box is 5 ft * 3 ft * 2 ft is to be filled with cubes that are 2in * 2in.Find the number of cubes it will take to fill this show your work and explain answers pleasee

b) if you reduced each dimension of the box by 25% what would the volume of the resulting box be? show your workk pleasee

c) you want to design a box with a volume of 125 cubic ft. give one possible dimensions for your box if all dimensions are integers?

Answer 1

a)
volume of box i 5*3*2=20 ft^3
volume of each cube is 2x2x2=8in^3
Convert the volume of cubes to square feet by dividing by 1728 in, which is (12 in)^3.
Each cube is (1/216)ft^3
To find the number of cubes that will fit into the box, divide the volume of the box by the volume of the cubes:
\[\frac{30}{\frac{1}{216}}=30(216)=6480 cubes\]

b)
Reduce each dimension by 25%; each dimension is 75% of its original.
\[(5)(.75)*3(.75)*2(.75)=\frac{405}{32}ft^3\]

c)
The obvious solution is to have each dimension as:
\[\sqrt[3]{125}=5\]
5ft x 5ft x 5ft

Answer 2

The volume of the box is 30ft^3, made a typo in the first part, but used 30 throughout the rest.