The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.
Step-by-step explanation:
The given is,
A prism of volume 15
A pyramid of the same height cut out
For the above question diagram is missing, so i attach the diagram.
Step:1
Ref the attachment,
Volume of figure = Volume of Prism - Volume of Pyramid....(1)
Step:2
From the given diagram,
Formula for volume of prism,
[tex]V_{prism} = whl[/tex]......................(2)
Where, w - Width of the prism
h - Height of prism
l - Length of prism
From the given,
Volume, V = 15 cubic units
l = a
w = b
h = c
Equation (1) becomes,
15 = abc
c = [tex]\frac{15}{ab}[/tex]
Step:3
Volume of pyramid, [tex]V = \frac{whl}{3}[/tex]..........................(2)
where,
w - Width of pyramid
h - Height of pyramid
l - Length of pyramid
From the given,
l = a
w = b
h = c
From the volume of prism, h = c = [tex]\frac{15}{ab}[/tex]
Equation (2) becomes,
[tex]V_{pyramid} = (\frac{ab}{3} )(\frac{15}{ab } )[/tex]
= 5
[tex]V_{pyramid} = 5[/tex] cubic units
Step:4
Equation (1) becomes,
Volume of figure = 15 - 5
= 10 cubic units
Result:
The volume of the figure is 10 cubic units, if a prism of volume 15 with a pyramid of the same height cut out.
