Question

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

Answer 1

Answer:

V = 10,240mm^3

Step-by-step explanation:

The volume of pyramid is given by the following formula:

$V=\frac{1}{3}bh$  (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):

$h=\sqrt{(34)^2-(16)^2}=30mm$

by replacing in (1) you obtain:

$V=\frac{1}{3}(32mm)^2(30mm)=10,240\ mm^3$

hence, the volume is 10240mm^3