Question

Hi!! Can you please help with this question and explain how to solve it??

Find the height in centimeters of a square pyramid with a volume of 144 cm3 and a base edge length equal to the height. Give the approximate answer rounded to 2 decimal places.

Answer 1

`7.56cm`

Explanation:

Given that,

base length = Height

so,

`volume = (1)/(3) {b}^(2) h \\`

We can also write this as( according to this question)

`v = (1)/(3) * {b}^(2) * b \\ v = \frac{ {b}^(3) }{3}`

let's solve

`v = \frac{ {b}^(3) }{3} \\ 144 = \frac{ {b}^(3) }{3} \\ 144 * 3 = {b}^(3) \\43 2 = {b}^(3) \\ \sqrt[3]{432} = b \\ b = 7.55`

`base = height = 7.55cm \\`

= 7.56cm

Answer 2

9514 1404 393

Answer:

7.56 cm

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.