# Can you find the volume?

## My teacher requires work to be shown, if its not too much trouble please show work!! thank you:)

Mar 2, 2017

$1104 c {m}^{3}$

#### Explanation:

Given that the dimensions of the box are 12cm by 12 cm by 5sm, it is a square box.

Volume of a square box is ${V}_{b} = {a}^{2} \times h '$
where $a$ is the side length and $h '$ is the height of the box.

$\implies {V}_{b} = {12}^{2} \times 5 = 720 c {m}^{3}$

Volume of a pyramid is ${V}_{p} = \frac{1}{3} \cdot b \cdot h$
where $b$ is the area of the base and $h$ is the height of the pyramid.
In this case, as the pyramid has a square base, $\implies b = {a}^{2}$.
Given that the slant height $s$ of the pyramid $= 10$
By Pythagorean theorem,
${s}^{2} = {\left(\frac{a}{2}\right)}^{2} + {h}^{2}$
$\implies h = \sqrt{{s}^{2} - {\left(\frac{a}{2}\right)}^{2}} = \sqrt{{10}^{2} - {\left(\frac{12}{2}\right)}^{2}} = \sqrt{64} = 8$
$\implies {V}_{p} = \frac{1}{3} \cdot {a}^{2} \cdot h = \frac{1}{3} \times {12}^{2} \times 8 = 384 c {m}^{3}$

Hence, volume of the object $= {V}_{b} + {V}_{p} = 720 + 384 = 1104 c {m}^{3}$