A piece of tin is in the form of a rectangle whose area is 486 sq. cm. A square side 3 cm is cut from each corner, and an open box is made by turning up the ends and sides. If the volume of the box formed is 756 cu. cm, what are the dimensions of the piece of tin?

Question

pooja195 · Answer

The initial dimensions of the piece are a and b, so that a*b = 486
On each side, you cut twice 3 cm, so you cut 6 cm, and the dimensions of the base of the box are
a-6 and b-6
The height of the box is of course 3, so that the volume of the box is :
(a-6)*(b-6)*3= 756

You have a system of equations

ab = 486
3(a-6)(b-6) = 756

Develop the second one
(a-6)(b-6) = 756 / 3 = 252
ab -6(a+b) + 36 = 252
ab - 6(a+b) = 252 - 36 = 216

You know that ab = 486, then

486 -6(a+b) = 216
6(a+b) = 486 - 216 = 270
(a+b) = 270 / 6 = 45

Now you have

ab = 486
a+b = 45

a = 45 - b
(45-b)b = 486
45b - b² = 486
b² -45b + 486 = 0

You solve with the quadratic formula anf you find 18

if b = 18, a = 487/18 = 27

18cm and 27 cm were the dimensions of the tin sheet !

pooja195 · Answer

do u get this