Question

what is the volume of this figure? 2 cm 3 cm 10 cm 11 cm 9 cm cubic centimeters

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the given 3 - D figure into two rectangular prisms. One with dimensions \(9\times10\times3\) and the other with dimensions \((11 - 9)\times10\times(2 + 3)\).

Step2: Calculate the volume of the first rectangular - prism

The volume formula for a rectangular prism is \(V_1=l\times w\times h\). For the first prism with \(l = 9\mathrm{cm}\), \(w = 10\mathrm{cm}\), and \(h = 3\mathrm{cm}\), we have \(V_1=9\times10\times3=270\mathrm{cm}^3\).

Step3: Calculate the volume of the second rectangular - prism

For the second prism, \(l=(11 - 9)=2\mathrm{cm}\), \(w = 10\mathrm{cm}\), and \(h=(2 + 3)=5\mathrm{cm}\). Using the volume formula \(V_2=l\times w\times h\), we get \(V_2=2\times10\times5 = 100\mathrm{cm}^3\).

Step4: Calculate the total volume

The total volume \(V\) of the figure is the sum of the volumes of the two prisms, \(V=V_1+V_2\). So \(V=270 + 100=370\mathrm{cm}^3\).

Answer:

370