Question

What is the volume of the square pyramid with base edges 32 mm and slant height 34 mm?

9,920 mm3



10,010 mm3



7,680 mm3



10,240 mm3

Answer 1

V = 10,240mm^3

Explanation:

The volume of pyramid is given by the following formula:

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

b: base of the pyramid = (32mm)^2

h: height

Thus, it is necessary to find the value of h, by using the Pitagoras's theorem, one half of the base and the slant height (which forms a rectangle triangle with h):

`h=√((34)^2-(16)^2)=30mm`

by replacing in (1) you obtain:

`V=(1)/(3)(32mm)^2(30mm)=10,240\ mm^3`

hence, the volume is 10240mm^3