Two rectangular pyramids are similar. The smaller pyramid has a volume of 12 cubic feet, and the larger pyramid has a volume of 324 cubic feet. If the smaller pyramid has a height of 6 feet,
what is the exact height (in feet) of the larger pyramid?

Volume of Big Pyramid= 324 cubic feet

Volume of small pyramid= 12

Volume of a pyramid is given as V=⅓xBasexheight

For the big pyramid

324=⅓xbasexheight

But 324= 27x12

Then for the big pyramid,

12=1/3x1/27xbasexheight

For the small pyramid

12=1/3xbasex6

Since both base are similar and from the equations derived so far

1/3x1/27xheight=1/3x6

Height=27x3x1/3x6=162feet