Can you find the volume?

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

1 Answer
Mar 2, 2017

1104 cm^31104cm3

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