Answer:
C. [tex]294.03 cm ^3[/tex]
Explanation:
We must find two volumes, that of the quadrangular prism and that of the pyramid of the top and finally add them to get the total volume.
Quadrangular prism volume:
[tex]V_{1}=A_{b}*H[/tex]
where
[tex]A_{b}[/tex] is the base area
and H is the height
[tex]V_{1}=6.7cm*6.2cm*5.5=228.47cm^3[/tex]
Volume of the quadrangular pyramid:
[tex]V_{2}=\frac{A_{b}*H}{3}[/tex]
To find the value of height H we use pitagoras:
[tex]h=\sqrt{5.8^2-(6.7/2)^2} =4.7347cm[/tex]
Thus
[tex]V_{2}=\frac{(6.7cm*6.2cm)*4.7347cm}{3}=65.56cm^3[/tex]
The total volume is :
[tex]V=V_{1}+V_{2}=228.27cm^3+65.56cm^3=294.03cm^3[/tex]
Wich is option C.
