The volume of a regular quadrangular technique is 8 em in a cube. What should be the side of the base of the prism

| February 15, 2021 | education

The volume of a regular quadrangular technique is 8 em in a cube. What should be the side of the base of the prism so that its total surface is the smallest?

To solve this task, we will need to remember the formula for the volume of a regular quadrangular prism.

So the formula for a regular quadrangular prism looks like this;

V = a * b * h, where a and b are the sides of the base, h is the height of the prism.

It is not difficult to see from the volume formula that the total volume consists of the base area multiplied by the height of the prism.

According to the condition of the problem, the minimum area of ​​the base of the prism is required, which means the product

a * b should be equal to 1, let’s write;

a * b = 1m2;

Then, from the volume formula, the height of the prism will be;

h = 8/1 = 8m.

Answer: the side of the base of the prism is 1m.



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