Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
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]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.