Respuesta :
The volume of Danny's pyramid is 176.8 cubic feet
The correct answer is an option (B)
What is square pyramid?
"It is a pyramid having square base."
What is the volume of the square pyramid?
Volume of square pyramid = [tex]\frac{1}{3}[/tex] × base area × height
What is the area of square?
A = [tex]a^{2}[/tex], where 'a' be the side length of the square
For given question,
Danny builds the pyramid to one-eightieth the size of Great Pyramids of Giza.
The Great Pyramid has a height of 480 feet and a square base with a side measuring 755 feet.
Let 'a' represents the side of a square base and 'h' represents the height of the pyramid build by Danny.
So, the side of a square base of Danny's pyramid measures,
[tex]\Rightarrow a = \frac{1}{80}\times 755\\\\\Rightarrow a=9.4~feet[/tex]
So, the base area of Danny's pyramid would be,
[tex]A=a^{2} \\\\A=(9.4)^2\\\\A=88.36\\\\A=88.4~~sq.~ft.[/tex]
And the height would be,
[tex]\Rightarrow h=\frac{1}{80}\times 480\\\\ \Rightarrow h=6~feet[/tex]
Using the formula of the volume of square pyramid,
[tex]\Rightarrow V=\frac{1}{3}\times 88.4\times 6\\\\ \Rightarrow V=176.8~~cu.~ft.[/tex]
Therefore, the volume of Danny's pyramid is 176.8 cubic feet
The correct answer is an option (B)
Learn more about the volume of the square pyramid here:
https://brainly.com/question/16139997
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