Answer :
The volume of the pyramid for a square base can be written as:
V = [tex] \frac{ s^{2}H }{3} [/tex]
First, get the volume of the first pyramid
V = ?
s = 20 in.
H = 21 in.
V = [tex]\frac{ 20^{2}(21)}{3}[/tex]
V = 2800 in³
Since, the volume of two pyramids are the same, we will equate it to equation 2
V = 2800 in³
s = ?
H = 84 in.
Applying it to the formula:
2800 = [tex]\frac{ s^{2}(84)}{3}[/tex]
[tex] \frac{(2800)(3)}{84} [/tex] = s² ⇒ combine like terms
100 = s² ⇒ get the square root of both sides to get the value of s
10 in = s ⇒side length of the base of the second pyramid
V = [tex] \frac{ s^{2}H }{3} [/tex]
First, get the volume of the first pyramid
V = ?
s = 20 in.
H = 21 in.
V = [tex]\frac{ 20^{2}(21)}{3}[/tex]
V = 2800 in³
Since, the volume of two pyramids are the same, we will equate it to equation 2
V = 2800 in³
s = ?
H = 84 in.
Applying it to the formula:
2800 = [tex]\frac{ s^{2}(84)}{3}[/tex]
[tex] \frac{(2800)(3)}{84} [/tex] = s² ⇒ combine like terms
100 = s² ⇒ get the square root of both sides to get the value of s
10 in = s ⇒side length of the base of the second pyramid