we know that
The volume of an oblique pentagonal prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base of the prism
h is the height of the prism
In this problem we have
[tex]B=15\ in^{2}[/tex]
[tex]h=3\ in[/tex]
so
The volume is equal to
[tex]V=(15)(3)[/tex]
[tex]V=45\ in^{3}[/tex]
Statements
case A) The volume of the prism is computed using the expression [tex](15)(3)[/tex]
The statement is true
See the procedure
case B) The volume cannot be determined because the dimensions of the base are unknown
The statement is false
Because, the dimensions of the base are not required, as the area of the base and the height of the prism are known
case C) The edge length can be used in place of the height of an oblique prism if the height is unknown
The statement is false
Because, the edge length and the height are different measures
case D)The unit on the volume measure of the prism is cubic inches
The statement is true
see the procedure
case E) The edge length times the height is the area of the base in any prism
The statement is false
Because, the edge length times the height is the lateral area of any prism
the answer is
The volume of the prism is computed using the expression [tex](15)(3)[/tex]
The unit on the volume measure of the prism is cubic inches
You can use the fact that even if the prism is oblique (its sides not being perpendicular to its base), we can deduce its volume by multiplying the height of the prism with the area of its base(in this pentagonal case or any such case where cross section of the prism parallel to base is of same area as that of the base and height measured is perpendicular to the base.
The correct options are:
Option A: - The volume of the prism is computed using the expression
(15)(3).
Option D: The unit on the volume measure of the prism is cubic inches.
The Volume of a pentagonal prism(both oblique and vertical) with base area of b sq. units and height of h units is given by
[tex]V = \text{Base Area\:} \times height = b\times h \: \rm unit^3[/tex]
The height needs to be measured vertically from the base. This is the exact reason why the third option is wrong. Third option is actually correct only for the case when prism is not oblique but vertical since in that case, both the edge length of the vertical sides and the height will be same.
Thus, for given prism, we have b = 15 sq inches and h = 3 inches
thus, Volume = (15)(3) = 45 cubic inches.
The correct options are:
Option A: - The volume of the prism is computed using the expression
(15)(3).
Option D: The unit on the volume measure of the prism is cubic inches.
Learn more about volume of pentagonal prism here:
https://brainly.com/question/4113799
