Please submit your concern

Explanation:

When the tin sheet is cut across its corners as shown in the figure, the box formed will have a height of x inches and its base will be a square of side (12 – 2x) inches.

Let the volume of the box, V = (12 – 2x)2 × x = 4x3 − 48x2 + 144x

For V to be maximum, dVdx shoule be 0.

i.e. 12x2 − 96x + 144 = 0

∴ 12(x − 6)(x − 2) = 0

∴ x = 2 or x = 6

However, x cannot be 6 as the length of the side is (12 – 2x).

∴ x = 2

Hence, option (d).

Alternatively,

Since V = (12 – 2x)2 × x = [2(6 – x)]2 × x = 4x(6 – x)2,

Substituting values of x from 1 to 5, we get V maximum when x = 2 (i.e. V = 128)

Feedback

Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.


© 2024 | All Rights Reserved | Apti4All