PreCalculus Questions

Question

A box is being constructed by cutting 3 inch squares from a rectangular sheet of cardboard that is 3 inches longer than it is wide. If the box is to have a volume of 324 cubic inches, find the dimensions of the sheet of cardboard.

18 in by 18 in
9 in by 36 in
159 in by 162 in
15 in by 18 in

Answer 1

√A box is being constructed by cutting 3 inch squares from a rectangular sheet of cardboard that is 3 inches longer than it is wide. If the box is to have a volume of 324 cubic inches, find the dimensions of the sheet of cardboard.

18 in by 18 in
9 in by 36 in
159 in by 162 in
15 in by 18 in

 

Solution:

 

The volume of the box is V = 324 in³. The box is a cube with volume

 

V=S³ where S is the length of the side S=³√ V = ³√ 324 = 6.87 in

 

the surface area of the box is six faces of A = S² = 6.87² = 47.2 in²

 

the total area needed to construct the box is = 6 x 47.2 in² = 283.2 in²

 

the length of the card board sheet is L = W+3 , Since L >W then it sis a rectangular shape. the required area of the cardboard sheet is

 

LW=283.2 in² ...eq1  and L=W+3 ...eq2 substitute 2nd eq into 1st eq

 

(W+3)W=283.2 , W²+3W=283.2,

 

W²+3W-283.2=0  Solve Quadratic equation

 

W=[-3±√(3)²-4(1)(-283.2)]/2 = [-3±√1141.8]/2=(-3±33.79)/2

 

Two roots,

W=(-3+33.79/2) and W =(-3-33.79/2)

W=15.4                    W=- 18.4

W should be positive W =15.4 in, L =W+3=15.4+3= 18.4in

 

 

The answer is 15 x 18 in