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Sagot :
The maximum dimensions (side length and height) of the pyramid for a given square base is equal to 6.99cm and 13.98cm respectively.
As given in the question,
Maximum amount of material used to cover sides of pyramid and its bottom = 250cm²
Surface area of the ( sides + bottom ) = 250cm²
Base is square :
Let 's' represent the the side length
Then height 'h' of the toy = 2 ( side length)
= 2s
Surface area of Pyramid = s² + 2s√(s²/4) + h²
⇒ 250 = s² + 2s√(s²/4) + (2s)²
⇒250 = s² + 2s√(s² + 16s²)/4
⇒250 = s² + 2s√17s²/4
⇒250 = s² + 2s(s/2)√17
⇒250 = s²+ s²√17
⇒250 = s² ( 1+ √17)
⇒250 = s²( 1 + 4.123 )
⇒ 250 = 5.123s²
⇒s² = 250/5.123
⇒ s= 6.99cm
Height 'h' = 2(6.99)
= 13.98cm
Therefore, the side-length and height of the pyramid with square base is equal to 6.99cm and 13.98cm respectively.
Learn more about pyramid here
brainly.com/question/17615619
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