Answer:
[tex] h = \frac{3V}{s^2} [/tex]
height (h) = 5 cm
Step-by-step explanation:
Volume of prism in terms of h (height):
[tex] V = \frac{1}{3}s^2h [/tex]
[tex] V = \frac{s^2h}{3} [/tex]
Multiply both sides by 3
[tex] V*3 = \frac{s^2h}{3}*3 [/tex]
[tex] 3V = s^2h [/tex]
Divide both sides by s^2
[tex] \frac{3V}{s^2} = \frac{s^2h}{s^2} [/tex]
[tex] \frac{3V}{s^2} = h [/tex]
[tex] h = \frac{3V}{s^2} [/tex]
Find height (h) given V = 60 cm³ and side length (s) = 6 cm. Plug the values into the formula above:
[tex] h = \frac{3(60)}{6^2} [/tex]
[tex] h = \frac{180}{36} [/tex]
[tex] h = 5 [/tex]
Height = 5 cm
