Question

what is the volume of this figure?
cubic centimeters

Explanation:

Step1: Divide the figure into two rectangular prisms

Let's split the L - shaped figure into two parts.

Step2: Calculate the volume of the first prism

The first prism has dimensions \(l = 1\space cm\), \(w=3\space cm\), \(h = 5\space cm\).
The volume formula for a rectangular prism is \(V=l\times w\times h\).
So, \(V_1=1\times3\times5 = 15\space cm^3\).

Step3: Calculate the volume of the second prism

The second prism has dimensions \(l=(4 - 1)=3\space cm\), \(w = 3\space cm\), \(h = 1\space cm\).
Using the volume formula \(V=l\times w\times h\), we get \(V_2=3\times3\times1=9\space cm^3\).

Step4: Sum the volumes of the two prisms

\(V = V_1+V_2\).
\(V=15 + 9\).

Answer:

\(24\)