Question

Can you find the volume?

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

Answer 1

`1104 cm^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^2xxh'`
where `a` is the side length and `h'` is the height of the box.

`=> V_b=12^2xx5=720 cm^3`

Volume of a pyramid is `V_p=1/3*b*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, `=> b=a^2`.
Given that the slant height `s` of the pyramid `=10`
By Pythagorean theorem,
`s^2=(a/2)^2+h^2`
`=> h=sqrt(s^2-(a/2)^2)=sqrt(10^2-(12/2)^2)=sqrt64=8`
`=> V_p=1/3*a^2*h=1/3xx12^2xx8=384 cm^3`

Hence, volume of the object `=V_b+V_p=720+384=1104cm^3`