Question

5. A cuboid has a total surface area of 150 cm² and is su-

(1) Show that the height, h cm, of the cuboid is given
(ii) Express the volume of the cuboid in terms of x.
(iii) Hence, determine, as x varies, its maximum volum

Answer 1

To determine the height of the cuboid given the surface area, solve the equation. Express the volume in terms of x and determine the maximum volume as x varies.

Step-by-step explanation:

To find the height of the cuboid given the total surface area, we need to solve for h in the equation

2lw + 2lh + 2wh = 150

Where l, w, and h represent the length, width, and height of the cuboid, respectively. Once the value of h is determined, we can use it to express the volume of the cuboid as V = lwh.

By differentiating V with respect to x and setting it equal to zero, we can find the maximum volume as x varies.

Learn more about Cuboid surface area and volume