Question

Find the height in centimeters of a square pyramid with a volume of 296 cm3 and a base edge length equal to the height. Give the approximate answer rounded to 2 decimal places.

Answer 1

We have a square pyramid with volume V = 296 cm³.

The base edge length is equal to the height.

We have to find the height of the pyramid.

We can express the volume as one third of the product of the base area and the heigth, so we can write:

`V=(1)/(3)A_b\cdot h=(1)/(3)b^2h`

As the base edge length b is equal to the height h, we can express the volume as:

`V=(1)/(3)b^2h=(1)/(3)h^2\cdot h=(h^3)/(3)`

As we know that V = 296 cm³, we can calculate h as:

`\begin{gathered} V=296 \\ (h^3)/(3)=296 \\ h^3=3\cdot296 \\ h^3=888 \\ h=\sqrt[3]{888} \\ h\approx9.61 \end{gathered}`

Answer: the height is approximately 9.61 cm.