Question

A planter in the shape of a cube has a volume of 1000in3 is the area of the base of the cube greater than or less than 1 square foot?explain

Answer 1

The cube volume is 10x10x10 inch3, so the base area is 10 inch x10 inch. On the other hand, we know that 1 square foot = 1 foot x 1 foot = 12 inch x 12 inch, so that is *greater* than the cube base.

Answer 2

area of the base of the cube is smaller than 1 square foot

Explanation:

since the volume of the cube is 1000 in^3 then its side must be (1000)^{1/3}

which is equal to 10 in

now, we know that area of the base of the cube will have an square cross section area= side^2

there area of base of the cube = 10^2= 100 sq in

now 1 foot= 12 in

therefore, 1 square foot = 12*12 square in = 144 sq in

clearly, area of the base of the cube is smaller than 1 square foot.

hope you liked the explanation.