Question

Question attached. Please and thank you.

Answer 1

ok, so the pyramids are similar, their heights are 8 and 24, small and large one


`\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{√(s^2)}{√(s^2)}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -----------------------------\\\\`

a)
their ratios
`\bf \cfrac{8}{24}\implies \cfrac{1}{3}`

so the small one is just 1/3 of the large one

b)


`\bf \cfrac{s^2}{s^2}\implies \cfrac{8^2}{24^2}\implies \cfrac{64}{576}\implies \cfrac{1}{9}`

c)


`\bf \cfrac{s^3}{s^3}\implies \cfrac{8^3}{24^3}\implies \cfrac{512}{13824}\implies \cfrac{1}{27}`

d)


`\bf \cfrac{v}{648}=\cfrac{8^3}{24^3}\implies \cfrac{v}{648}=\cfrac{512}{13824}`

solve for "v"