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Sagot :
volume of pyramid = 1/3 b2h
volume of cube = b3
now , provided pyramid and cube have same edges and same heights.
thus, volume of pyramid = 1/3 b3
volume of cube = b3.
thus, ratio = 1/3b3/ b3 = 1/3.
Thus, volume of pyramid = 1/3volume of cube
volume of cube = b3
now , provided pyramid and cube have same edges and same heights.
thus, volume of pyramid = 1/3 b3
volume of cube = b3.
thus, ratio = 1/3b3/ b3 = 1/3.
Thus, volume of pyramid = 1/3volume of cube
[tex]V_{cube}=a^3\ \ \ and\ \ \ V_{pyramid}= \frac{1}{3} \cdot a^2\cdot h=\frac{1}{3}a^3\\ \\ \frac{V_{pyramid}}{V_{cube}} = \frac{\frac{1}{3}a^3}{a^3}= \frac{1}{3}\\ \\ \\A_{cube}=6a^2\\ \\h^2=a^2+( \frac{1}{2} a)^2\ \ \ \Rightarrow\ \ \ h^2= \frac{5a^2}{4}\ \ \ \Rightarrow\ \ \ h= \frac{a \sqrt{5} }{2}\\\\A_{pyramid}=a^2+4\cdot \frac{1}{2}ah=a^2+2a\cdot \frac{a \sqrt{5} }{2} =a^2(1+ \sqrt{5}) \\ \\ \frac{A_{pyramid}}{A_{cube}}= \frac{a^2(1+ \sqrt{5}) }{6a^2} = \frac{1+ \sqrt{5}}{6}[/tex]
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