Thread: volume of a pyramid (not so easy)

1. volume of a pyramid (not so easy)

Want a challenge ? Well I got one. It got me thinking for 2 days and got nothing ...

A plane is passed parallel to the base and 8 cm from the vertex of a pyramid whose base is 45 square cm and whose altitude is 12 cm. What is the volume of that part of the pyramid after the top had been removed ?

2. Originally Posted by SamanthaMathGirl
A plane is passed parallel to the base and 8 cm from the vertex of a pyramid whose base is 45 square cm and whose altitude is 12 cm. What is the volume of that part of the pyramid after the top had been removed ?
volume of the large pyramid should be no problem, correct?

the parallel plane cuts off a smaller similar pyramid on top whose height is 8 cm.

since the two pyramids are similar, their respective volumes will be in the ratio $\displaystyle \frac{8^3}{12^3}$

use the above ratio to determine the volume of the smaller pyramid ... you should be able to finish from there.