Question

1. show and explain how you would find the volume of this solid figure. not to scale v = lxwxh 8cm 5cm 3cm 10cm 9cm

Explanation:

Step1: Divide the figure into two rectangular prisms

We can consider one prism with dimensions \(9\times10\times3\) and another with dimensions \((9 - 5)\times10\times(8 - 3)\)

Step2: Calculate volume of first prism

Using the formula \(V = l\times w\times h\), for the first prism with \(l = 9\mathrm{cm}\), \(w=10\mathrm{cm}\), \(h = 3\mathrm{cm}\), we have \(V_1=9\times10\times3=270\mathrm{cm}^3\)

Step3: Calculate volume of second prism

The second prism has \(l=(9 - 5)=4\mathrm{cm}\), \(w = 10\mathrm{cm}\), \(h=(8 - 3)=5\mathrm{cm}\). Using the volume formula \(V = l\times w\times h\), we get \(V_2=4\times10\times5 = 200\mathrm{cm}^3\)

Step4: Find total volume

The total volume \(V\) of the solid figure is the sum of the volumes of the two prisms. So \(V=V_1 + V_2=270+200 = 470\mathrm{cm}^3\)

Answer:

\(470\mathrm{cm}^3\)