Question

For a cuboidal jewellery metal box to satisfy certain requirements, its length must be three meter greater than the width, and its

height must be two meter less than the width.

(i) Write down length and height of the box in terms of its width. (1)

(ii) What will be the lateral surface area of the box? (1)

(iii) What will be the total surface area of the box? (1)

(iv) Find out the volume of the box.​

Answer 1

Answer:

Answer

Correct option is

C

2 inch

Length of the Cuboid = 24−2x

Breadth of Cuboid =9−2x

Height of Cuboid =x

Volume of Cuboid V=(24−2x)(9−2x)x

V=216x+4x

3

−66x

2

To know the volume maximum

dx

dV

=0

⇒

dx

dV

=216+12x

2

−132x=0

⇒

dx

dV

=18+x

2

−11x=0

(x−9)(x−2)=0

x=9 or 2

By substituting 9 and 2 we get maximum value of volume for x=2inch