Question

pre - algebra ic sem 2 fall 2025
semester a
what is the volume of the given figure, in cubic centimeters?
1,080
936
1,008
756

Explanation:

Step1: Calculate the volume of the large cuboid

The formula for the volume of a cuboid is \(V = l\times w\times h\). For the large cuboid, \(l = 10\space cm\), \(w=9\space cm\), \(h = 10\space cm\). So \(V_1=10\times9\times10 = 900\space cm^3\)

Step2: Calculate the volume of the small cuboid

The height of the small cuboid is \(10 - 2=8\space cm\) (since the total height is \(10\space cm\) and the height of the upper - part is \(2\space cm\)). The length of the small cuboid is \(12 - 10 = 2\space cm\), width \(w = 9\space cm\), height \(h=2\space cm\). Using the volume formula \(V=l\times w\times h\), we get \(V_2=(12 - 10)\times9\times2= 36\space cm^3\)

Step3: Calculate the volume of the bottom - layer cuboid

The length \(l = 12\space cm\), width \(w = 9\space cm\), height \(h = 2\space cm\). Using the volume formula \(V=l\times w\times h\), we get \(V_3=12\times9\times2=216\space cm^3\)

Step4: Calculate the total volume

The total volume \(V = V_1+V_2+V_3\). Substitute the values: \(V=900 + 36+216=1008\space cm^3\)

Answer:

\(1008\)