The volume of a shape is the amount of space in it
The volume of the pyramid is: (a) [tex]\mathbf{V_p =\frac 16 (b)(b)(2h)}[/tex] or [tex]\mathbf{V_p =\frac 13 Bh}[/tex]
The volume of the cube is given as:
[tex]\mathbf{V_c = (b)(b)(b)}[/tex]
Where:
[tex]\mathbf{b =2h}[/tex]
So, we have:
[tex]\mathbf{V_c = (b)(b)(2h)}[/tex]
The volume of the pyramid is:
[tex]\mathbf{V_p = \frac{1}{6}V_c}[/tex]
This gives
[tex]\mathbf{V_p =\frac 16 (b)(b)(2h)}[/tex]
Divide 6 and 2 by 2
[tex]\mathbf{V_p =\frac 13 (b)(b)(h)}[/tex]
The base area of the cube is:
[tex]\mathbf{B = (b)(b)}[/tex]
So, we have:
[tex]\mathbf{V_p =\frac 13 Bh}[/tex]
Hence, the volume of the pyramid is:
(a) [tex]\mathbf{V_p =\frac 16 (b)(b)(2h)}[/tex] or [tex]\mathbf{V_p =\frac 13 Bh}[/tex]
Read more about volumes of pyramid at:
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