Two similar pyramids have surface areas 200 m 2 and 500 m 2 . The smaller pyramid has volume 500 m ​3 . Find the volume of the larger pyramid.

Two similar pyramids have surface areas 200 m2 and 500 m2. The smaller pyramid has volume 500 m3. Find the volume of the larger pyramid.

They are really cool pics omi,  let me see if I get the same answer.

Two similar pyramids have surface areas 200 m2 and 500 m2. The smaller pyramid has volume 500 m3. Find the volume of the larger pyramid.

ratio of areas is     200:500     =       \( 2 : 5\)

ratio of sides is                             \(\sqrt2:\sqrt5\)

ratio of volume is                       \(2\sqrt2:5\sqrt5\)

so if small volume is 500m^3

then

\(\frac{5\sqrt5}{2\sqrt2}=\frac{x}{500}\\ x=\frac{500*5\sqrt5}{2\sqrt2}\\ x=\frac{1250\sqrt5}{\sqrt2}\\ x=\frac{1250\sqrt{10}}{2}\\ x=625\sqrt{10}\\ big\;volume\;\approx 1976.42m^2\)