Math CentralQuandaries & Queries


Question from Malik:

A company wants to alter the dimension of container. The new container is in the shape of right prism equivalent to the current one.
The current container has height of 12cm and square base. The new container has also square base, but in the dimension base is increased by 3cm and height is decreased by 5cm.
if the cardboard is used to manufacture the new container, what area of cardboard is used to make new container


The volume of a right prism is the area of the base times the height. If the length of a side of the new container is x cm then the length of a side of the old container is x - 3 cm. Since the volumes of the two containers are the same

(x - 3)2 × 12 = x2 × (12 - 5)

Solve this equation for x.

There are 6 pieces of cardboard required to make the container. Find the sum of the areas of the 6 pieces.


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