Hello!
To find the volume of a square pyramid, use the formula: V = 1/3b²h.
In this formula, b is a side length of the base, and h is height of the figure.
Figure 1
Since we are given the side length of the base, which is 18 inches, and the height, which is 12 inches, we can find the volume.
V = 1/3(18)²(12)
V = 1/3(324)(12)
V = 108(12)
V = 1296 inches³.
The volume of the first figure is 1296 inches cubed.
Figure 2
Since we are not given the height of this figure, we need to find it using the pythagorean theorem. In this case, we need to find a and b. Since the base of this triangle is a square, to find b, it is half the side length of the base.
22 inches / 2 = 11 inches
With the value of b, we can find the height, or a.
a² + 11² = 24²
a² + 121 = 567 (subtract 121 from both sides)
a² = 455 (take the square root of both sides)
a = √455
With the height being √455, we can find the volume.
V = 1/3(22)²(√455)
V = 1/3(484)(√455)
V = (484/3)(√455)
V = 3441.3576..
This can be rounded to 3441.36 inches cubed.
Therefore, the volume of figure two is 3441.36 inches cubed.
