Question

Q18. An online retail company ships its products in the cartons.
Each of the cartons is made by a rectangular sheet of fiberboard with dimensions of 8 m by 3 m
While making the carton, equal squares of side length 'x' metres are cut-off from each corner
of the rectangular sheet of fiberboard. After that, the resulting flaps are folded up to form the
carton.
See the figure given below to identify the sides of the carton.
X
х
X
X
х
х
Based on the above information, answer the following:
(0) The volume V of the carton is given by V=f(x), then f(x) equals
(a) 22x - 24x² + 4x
1 1 1
(b)
X + X
24 22
4
(c) 24x + 22x2 - 4x
(d) 24x - 22x² + 4x?
12292
]
n​

Answer 1

Given : cartons is made by a rectangular sheet of fiberboard with dimensions of 8 m by 3 m

While making the carton, equal squares of side length 'x' metres are cut-off from each corner  of the rectangular sheet of fiberboard.

To Find :  Volume of the box

a) 22x - 24x² + 4x ³

(b)  24x + 22x² + 4x ³

(c) 24x + 22x² - 4x³

(d) 24x - 22x² + 4x³

Solution:

rectangular sheet of fiberboard with dimensions of 8 m by 3 m

Each side = 8 - 2x   and  3 - 2x

Height = x

Volume = x ( 8 - 2x)(3 - 2x)

= x ( 24 - 16x - 6x + 4x²)

= x( 24 - 22x + 4x²)

= 24x - 22x² + 4x³

Learn More:

An open box is to be made from a square piece of material, 24 cm ...

brainly.in/question/9492013

Find the number of cubical boxes of edge 3 cm that can be packed in a

brainly.in/question/13999508