Choose any volume for the cuboid
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Choose any volume for the cuboid

TASK 2

Figure 1 shows a solid cuboid with a square base of side x metres and height h metres.


[a] Choose any volume for the cuboid. Write the height of the cuboid, h, in terms of x.

[b] Write the surface area, A, of the cuboid in terms of x.

(c) Use calculus to find the value of x which gives the minimum surface area.

[d) Find this minimum surface area. What do you notice?

[e] Repeat for different volumes.

[f] Investigate further.

Hint
Mathematics"A surface area, on a 3D shape, is the sum of the areas of all the surfaces or the faces. Now, a cuboid contains 6 rectangular faces and to find it's surface area, the areas of all 6 surfaces or faces needs to be added. Another way to find it is to label the length (l), width (w), and height (h) of the prism and then use the formula, i.e. SA (Surface area) = 2lw (length*widht) + 2l...
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