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# Calculus problem

An open container is such that each horizontal cross section is an equilateral triangle. its base has side of a length 10cm and its top has sides length 10x cm. each sloping edge has length 20cm. the surface of the container is modelled by part of an inverted triangular pyramid.

the capacity V(x) litres is :

V(x)=1/12 (x^2 +x +1) sqrt(12-(x-1)^2)
CONDITION:(x is greater than or equal to zero and less than or equal to (1+ 2xsqrt(3))

A) Explain why the condition is placed at the end of the formula.

B) Find the maximum possible capacity of the container according to the model. (please could you explain your answer).

#### Solution Preview

Please see the attached file.

An open container is such that each horizontal cross section is an equilateral triangle. its base has side of a length 10cm and its top has sides length 10x cm. each sloping edge has length 20cm. the surface of the container is modelled by part of an inverted triangular pyramid.

the capacity V(x) ...

#### Solution Summary

This solution is comprised of a detailed explanation to explain why the condition is placed at the end of the formula.

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