Question

Victor needs to find the volume of 6 cubeshaped boxes with sides lengths of between 2 feet and 7 feet. The side lengths of the boxes can only be whole numbers. The volume of a cube-shaped box with a side length of s is given by the function V(s) = s 3 .

Answer 1

The volume of 6 cube shaped boxes with length {2, 3, 4, 5, 6, 7} is {8, 27, 64, 125,21 6, 343} feet respectively.

Explanation:

Consider the provided information.

Victor needs to find the volume of 6 cube shaped boxes with sides lengths of between 2 feet and 7 feet.

The side lengths of the boxes can only be whole numbers.

As the side lengths can be whole numbers, so the whole number between 2 and 7 is: 2, 3, 4, 5, 6 and 7.

The least length for side is 2 feet and the greatest length for side is 7 feet.

The volume of the cube shaped is:
`V(s)=s^3`, where s is the side.

For side = 2 feet

Substitute s=2 in above formula.

`V(s)=2^3`

`V(s)=8`

For side = 3 feet

Substitute s=2 in above formula.

`V(s)=3^3`

`V(s)=27`

For side = 4 feet

Substitute s=2 in above formula.

`V(s)=4^3`

`V(s)=64`

For side = 5 feet

Substitute s=5 in above formula.

`V(s)=5^3`

`V(s)=125`

For side = 6 feet

Substitute s=6 in above formula.

`V(s)=6^3`

`V(s)=216`

For side = 7 feet

Substitute s=7 in above formula.

`V(s)=7^3`

`V(s)=343`

Hence, the volume of 6 cube shaped boxes with length {2, 3, 4, 5, 6, 7} is {8, 27, 64, 125,21 6, 343} feet respectively.

Answer 2

V(s) = (S)^3
6 cube shapes with sides ranging in whole numbers from 2 feet to 7 feet:
S1 = 2 feet, S2 = 3 feet, S3 = 4 feet, S4 = 5 feet, S5 = 6 feet, S6 = 7 feet
V(s)1 = (S1)^3 = (2)^3 = 8 cubic feet
V(s)2 = (S2)^3 = (3)^3 = 27 cubic feet
V(s)3 = (S3)^3 = (4)^3 = 64 cubic feet
V(s)4 = (S4)^3 = (5)^3 = 125 cubic feet
V(s)5 = (S5)^3 = (6)^3 = 216 cubic feet
V(s)6 = (S6)^3 = (7)^3 = 343 cubic feet