What is the surface area of an open box with a square base that has a volume of 5000 cubic inches and each side of the square has is 10 inches long.
2 Answers
sciencesolve | Teacher | (Level 3) Educator Emeritus
The problem requests for you to evaluate the surface area of the opened square base box, hence, you need to use the following formula, such that:
`SA = x^2 + 4x*y`
`x^2 ` represents the area of square base
`x*y` represents the area of one side of box (there exists 4 sides)
The problem provides the length of square x = 10 inches, such that:
`SA = 10^2 + 40*y`
The problem provides the volume of box, hence, using the formula of volume, yields:
`V = x^2*y => 5000 = 100*y => y = 50` inches
You need to replace 50 for y in equation of surface area, such that:
`SA = 100 + 40*50 => SA = 2100` square inches
Hence, evaluating the surface area of the opened square base box, under the given conditions, yields `SA = 2100` square inches.
justaguide | College Teacher | (Level 2) Distinguished Educator
The area of the base of the open box is 5000 cubic inches. The length of each side of the square base is 10 inches.
If the height of the box is h, the volume is 10^2*h.
Equating 100*h to the volume gives 100*h = 5000
=> h = 50
The surface area of the open box is 50*10*4 + 100 = 2100 square inches.