Answer:
C. \(294.03 cm ^3\)
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:
\(V_{1}=A_{b}*H\)
where
\(A_{b}\) is the base area
and H is the height
\(V_{1}=6.7cm*6.2cm*5.5=228.47cm^3\)
Volume of the quadrangular pyramid:
\(V_{2}=\frac{A_{b}*H}{3}\)
To find the value of height H we use pitagoras:
\(h=\sqrt{5.8^2-(6.7/2)^2} =4.7347cm\)
Thus
\(V_{2}=\frac{(6.7cm*6.2cm)*4.7347cm}{3}=65.56cm^3\)
The total volume is :
\(V=V_{1}+V_{2}=228.27cm^3+65.56cm^3=294.03cm^3\)
Wich is option C.
