13. A person wants to make an open box by cutting equal squares from the corners of a piece of metal 160 cm by 240 cm as shown in Figure below. If the edge of each cut-out square is x cm, find the volume of the box, when x = 1 and x = 3

Question

29-12-2023
Mathematics

Answered

13. A person wants to make an open box by cutting equal squares from the corners of a piece of metal 160 cm by 240 cm as shown in Figure below. If the edge of each cut-out square is x cm, find the volume of the box, when x = 1 and x = 3

Answer :

Other Questions

Assuming an initial bracket of (1.16,5.3), the first iterative value of the root of t−ᵗ−0.3=0 using the bisection method is

sqdancefan sqdancefan · Answer 1 · 2023-12-29T15:30:07-05:00

Answer:

37604 cm³ when x=1
108108 cm³ when x=3

Step-by-step explanation:

You want the volume of an open box folded from a 160 cm by 240 cm rectangle with squares of side x cut from the corners. The values of interest are x=1 and x=3.

Volume

The base of the box will have dimensions (160 -2x) and (240 -2x) cm. So, the volume is ...

V(x) = x(160 -2x)(240 -2x) = 4x(80 -x)(120 -x)

The volume for x=1 is ...

V(1) = 4(1)(79)(119) = 37604 . . . . cm³

The volume for x=3 is ...

V(3) = 4(3)(77)(117) = 108108 . . . . cm³