Answer:
Step-by-step explanation:
The volume of a pyramid is:
where is the area of the base and
is the height (the perpendicular measurement between base and highest point, not the slant height)
Since the base is a square, the area is given by:
where is the length of the side:
, thus:
Now we need to find the height, for this we use the right triangle that forms with half of a square side (8in/2 = 4in), the slant height (10in), and the height.
In this right triangle, the slant height is the hypotenuse, the leg 1 is the unknown height, and leg 2 is half of the square side.
Using pythagoras:
substituting our values, and indicating that leg 1 is height h:
and solving for the height:
and finally we calculate the volume using this height and the area of the base:
rounding to the nearest cubic inch: