Hi!! Can you please help with this question and explain how to solve it??
2 answers:
9514 1404 393
Answer:
7.56 cm
Step-by-step explanation:
The volume is given by the formula ...
V = 1/3b²h . . . . where b is the base edge length, and h is the height.
Here we have V = 144 cm³, and b = h. Filling in these values and solving for h, we get ...
144 cm³ = 1/3h³
432 cm³ = h³
h = ∛432 cm ≈ 7.55953 cm
The height of the pyramid is about 7.56 cm.
Answer:
![7.56cm](https://tex.z-dn.net/?f=7.56cm)
Step-by-step explanation:
Given that,
base length = Height
so,
![volume = \frac{1}{3} {b}^{2} h \\](https://tex.z-dn.net/?f=volume%20%3D%20%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%7Bb%7D%5E%7B2%7D%20h%20%5C%5C%20%20)
We can also write this as( according to this question)
![v = \frac{1}{3} \times {b}^{2} \times b \\ v = \frac{ {b}^{3} }{3}](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20%20%20%7Bb%7D%5E%7B2%7D%20%20%5Ctimes%20b%20%5C%5C%20v%20%3D%20%20%20%5Cfrac%7B%20%7Bb%7D%5E%7B3%7D%20%7D%7B3%7D%20%20)
let's solve
![v = \frac{ {b}^{3} }{3} \\ 144 = \frac{ {b}^{3} }{3} \\ 144 \times 3 = {b}^{3} \\43 2 = {b}^{3} \\ \sqrt[3]{432} = b \\ b = 7.55](https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B%20%7Bb%7D%5E%7B3%7D%20%7D%7B3%7D%20%20%5C%5C%20144%20%20%3D%20%20%5Cfrac%7B%20%7Bb%7D%5E%7B3%7D%20%7D%7B3%7D%20%20%5C%5C%20144%20%5Ctimes%203%20%3D%20%20%7Bb%7D%5E%7B3%7D%20%20%5C%5C43%202%20%3D%20%20%7Bb%7D%5E%7B3%7D%20%20%5C%5C%20%20%5Csqrt%5B3%5D%7B432%7D%20%20%3D%20b%20%5C%5C%20b%20%3D%207.55)
![base = height = 7.55cm \\](https://tex.z-dn.net/?f=base%20%3D%20height%20%3D%207.55cm%20%5C%5C%20)
= 7.56cm
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Step-by-step explanation:
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