Question

What is the volume of the square pyramid with base edges 60 in. and slant height 50 in.?

Answer 1

V= area of the base * height
Finding the height of the pyramid: use Pythagorean theorem
First divide the base edge by 2. That way you can use the theorem
30^2 +b^2 = 50^2
900+b^2= 2500
900-900+b^2=2500-900
b^2=1600

`\sqrt{b {}^(2) } = √(1600)`
b=40 in
Now on to the volume
V=60*60*40
V=3600*30
V=144000 in cubed
The volume is 140,000 inches cubed

Answer 2

Answer: 48000 cubic inches

Explanation:

Given: Slant height of pyramid (l)= 50 in.

Base edge (s)= 60 in.

Let h be the height of the pyramid, the to find the height of the pyramid we consider a portion of pyramid as right triangle, so by Pythagoras theorem we have

`h=\sqrt{l^2-((s)/(2))^2}\\\\\Rightarrow\ h=\sqrt{(50)^2-((60)/(2))^2}\\\\\Rightarrow\ h=40\ in.`

The volume of square pyramid is given by :-

`V=(1)/(3)s^2h\\\\\Rightarrow\ V=(1)/(3)*(60)^2(40)\\\\\Rightarrow\ V=48000\ in.^3`