Question

From each corner of a square sheet of side 8 cm, a square of side y cm is cut. The remaining sheet is folded into a cuboid. The minimum possible vol ume of the cuboid formed is M cubic cm. If y is an integer, then find M

Answer 1

Answer:

The value of M = 12cubic cm

Step-by-step explanation:

Volume of cube with side 'a' is given by

volume V =a³

Volume of cuboid with length 'a', breadth  'b' and height 'h'

Volume V = abh

To find the minimum volume

The possible values of y are 1, 2 and 3

case 1

if y =1 then a = 8-2 = 6, b= 6 and h= 1

V1 = 6x6x1 = 36 cubic cm

case 2

if y =2 then a = 8-4 = 4, b= 4 and h= 2

V1 = 4x4x2 = 32 cubic cm

case 3

if y =3 then a = 8-6 = 2, b= 2 and h=3

V1 = 2x2x3 = 12 cubic cm

Therefore minimum volume be 12 cubic cm

M = 12 cubic cm

Answer 2

Step-by-step explanation:

length =breadth=(8-2y)cm and height y cm.

volume = (8-2y)(8-2y)y

(8-2y)^2(y)

8-2y>0 I.e, y<4 and y is an integer

y=1,2,3

Among these value of y , volume is minimum when y =3

then, volume =12cm^3

Hence M =12.