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

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 2

Answer:

$7.56cm$

Step-by-step explanation:

Given that,

base length = Height

so,

$volume = \frac{1}{3} {b}^{2} h$

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

$v = \frac{1}{3} \times {b}^{2} \times b \\ v = \frac{ {b}^{3} }{3}$

let's solve

$v = \frac{ {b}^{3} }{3} \\ 144 = \frac{ {b}^{3} }{3} \\ 144 \times 3 = {b}^{3} \\43 2 = {b}^{3} \\ \sqrt[3]{432} = b \\ b = 7.55$

$base = height = 7.55cm$

= 7.56cm