SOLUTION: A planter in the shape of a cube has a volume of 1,000 in.^3 is the area of the base of the cube greater than or less than 1 square foot? Explain

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A planter in the shape of a cube has a volume of 1,000 in.^3 is the area of the base of the cube greater than or less than 1 square foot? Explain       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1095551: A planter in the shape of a cube has a volume of 1,000 in.^3 is the area of the base of the cube greater than or less than 1 square foot? Explain
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the planter has a volume of 1000 cubic inches.

this means each side of the planter has a length of 10 inches because the cube root of 1000 is equal to 10.

the volume of a cube is the length of a side raised to the third power.

you can use the length of any side because all of the sides have the same length.

10^3 = 1000 cubic inches.

the area of a face of the cube is equal to the length of a side raised to the second power.

10^2 = 100 square inches.

the area of the base of the cube is the area of any of the faces of the cube since all faces of the cube have the same area.

a square foot is equal to 12 inches by 12 inches = 144 square inches.

100 square inches is less than 144 square inches.

therefore the area of the base of the cube is less than a square foot.