wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A box is constructed from a rectangular metal sheet of 21 cm. by 16 cm, by cutting equal squares of sides x from the corners of the sheet and then turning up the projected portions. For what values of x the volume of the box will be maximum?

A
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
3
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
5
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 3
Let the dimensions of the box after cutting equal squares of side x on the corner will be
212x,162x and height x
V=x(212x)(162x)
V=x(33674x+4x2)
V=4x374x2+336x
dVdx=12x2148x+336

For maximum or minimum,
dVdx=0
dVdx=12x2148x+336=0
or 3x237x+84=0.
(x3)(3x+28)=0
x=3 (x=283, not possible )

Now, d2Vdx2=6x37=1837
=19=ive for x=3.
Hence V is maximum when x=3

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Approximating Decimals
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon