Question

A regular square pyramid has base edges of length 16 and its lateral faces are inclined 30­° to the base of the pyramid. What is the: 1) height of the pyramid? 2) volume of the pyramid?

Answer 1

1)
`h=(8√(3))/(3)\ units`

2)
`V=(2,048√(3))/(9)\ units^3`

Explanation:

Part 1) Find the height of the pyramid

we know that

`tan(30^o)=(h)/((b/2))`

where

h is the height of the pyramid

b is the length side of the square base

we have

`tan(30^o)=(√(3))/(3)`

`b=16\ units`

substitute

`(√(3))/(3)=(h)/((16/2))`

`(√(3))/(3)=(h)/(8)`

`h=(8√(3))/(3)\ units`

Part 2) Find the volume of the pyramid

we know that

The volume of the pyramid is equal to

`V=(1)/(3) Bh`

where

B is the area of the square base

h is the height of the pyramid

we have

`B=(16^2)=256\ units^2`

`h=(8√(3))/(3)\ units`

substitute

`V=(1)/(3) (256)((8√(3))/(3))`

`V=(2,048√(3))/(9)\ units^3`