Question

if a = 4 units, b = 6 units, and c = 10 units, what is the volume of the three prisms above?
a. 240 cubic units
b. 320 cubic units
c. 256 cubic units
d. 268 cubic units
note: figure is not drawn to scale.

Explanation:

Step1: Calculate the volume of the first prism

The first prism has dimensions \(a\times a\times c\). Substitute \(a = 4\), \(c=10\).
Volume \(V_1=a\times a\times c=4\times4\times10 = 160\)

Step2: Calculate the volume of the second prism

The second prism has dimensions \(a\times a\times b\). Substitute \(a = 4\), \(b = 6\).
Volume \(V_2=a\times a\times b=4\times4\times6=96\)

Step3: Calculate the volume of the third prism

The third prism has dimensions \(a\times a\times a\). Substitute \(a = 4\).
Volume \(V_3=a\times a\times a=4\times4\times4 = 64\)

Step4: Calculate the total volume

Total volume \(V=V_1 + V_2+V_3\)
\(V=160 + 96+64=320\)

Answer:

B. 320 cubic units