Question

A box is created from a sheet of cardboard 25 inch on a side by

cutting a square from each corner and folding up the sides .Let x

represent the length of the sides of the squares removed from each

corner .If area of the sides of the box is 13 square inch, give the

answer of the following questions.
(i)the volume of the box can be expressed by

(a) x 2 X 25

(b) x3

(c)4 x3 +100x 2 + 625

(d) 4 x3

- 100x 2 + 625x

(ii) If area of the sides (walls) of the box are 12 square inch then value

of x is

(a) 13 inch

(b) 1 inch

(c)0.5 inch

(d) 24 inch

(iii) the area of the bottom of the box is

(a)625 sq. Inch

(b)576 sq. Inch

(c)529 sq. Inch

(d) 169 sq. Inch

(iv) the volume of the box is

(a) 24 X 24 X 0.5

(b)24 X 24 X 1

(c) 13 X 13 X 12

(d)12 X !2 X 13

(v) The graph of the volume represented, will intersect the X-axis in

point(s)

(a) Zero

(b)Two

(c)One

(d) Three
​

Answer 1

Given : A box is created from a sheet of cardboard 25 inch on a side by

cutting a square from each corner and folding up the sides

x  represent the length of the sides of the squares removed from each  corner

To Find : the volume of the box can be expressed by

If area of the sides (walls) of the box are 12 square inch then value  of x is

the area of the bottom of the box

volume of the box

The graph of the volume represented, will intersect the X-axis in  point(s)

Solution:

Side = 25 inch

x is cut from each side

Hence remaining side length = 25 - 2x

Height = x

Volume = ( 25 - 2x)² * x

= (625 + 4x² - 100x)x

= 4x³ - 100x² + 625

volume of the box can be expressed by 4x³ - 100x² + 625

area of the sides (walls) of the box are 12 square inch then value

area of the sides (walls)  = (25 - 2x) x

(25 - 2x) x = 12

=> 2x² - 25x + 12 = 0

=> 2x² - 24x -x + 12 = 0

=> 2x(x - 12)- 1(x - 12) = 0

=> (2x - 1)(x - 12) = 0

=> x = 1/2  or x = 12

=> x = 0.5 from given options

area of the bottom of the box = (25 - 2x)² = 24² = 576 sq inch

volume of the box is 24 x 24 x 0.5

graph of the volume represented, will intersect the X-axis in 3 points

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