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A toy is being constructed in the shape of a pyramid. The maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters. The height of the toy is double the side length. What are the maximum dimensions to the nearest square centimeter for a square base and for a hexagonal base?

\begin{tabular}{|c|c|c|}
\hline
Shape of Base & Side Length & Height \\
\hline
square & [tex]$\square$[/tex] cm & [tex]$\square$[/tex] cm \\
\hline
regular hexagon & [tex]$\square$[/tex] cm & [tex]$\square$[/tex] cm \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
Let's go through the solution step by step for both shapes: the square base and the hexagonal base.

1. Square Base Pyramid:
- The height of the pyramid is double the side length of the base.
- Given that the total surface area (including the base and four triangular faces) is 250 square centimeters.
- Based on this information, we find:
- Side length = 7 cm
- Height = 14 cm

2. Hexagonal Base Pyramid:
- Again, the height of the pyramid is double the side length of the base.
- The total surface area (including the base and six triangular faces) must add up to 250 square centimeters.
- From this, we determine:
- Side length = 5 cm
- Height = 11 cm

So, the maximum dimensions of the toy to the nearest square centimeter are:
\begin{tabular}{|c|c|c|}
\hline
Shape of Base & Side Length & Height \\
\hline
square & 7 cm & 14 cm \\
\hline
regular hexagon & 5 cm & 11 cm \\
\hline
\end{tabular}
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