what is the volume of this figure? cubic centimeters

Answer

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the given figure into two rectangular - prisms. One on the top with dimensions (l_1 = 10\mathrm{cm}), (w_1 = 3\mathrm{cm}), (h_1=(9 - 2)\mathrm{cm}=7\mathrm{cm}), and the other on the bottom with dimensions (l_2 = 10\mathrm{cm}), (w_2 = 11\mathrm{cm}), (h_2 = 2\mathrm{cm}).

Step2: Calculate the volume of the top rectangular - prism

The volume formula for a rectangular - prism is (V=l\times w\times h). For the top prism, (V_1=l_1\times w_1\times h_1). Substituting the values: (V_1 = 10\times3\times7=210\mathrm{cm}^3).

Step3: Calculate the volume of the bottom rectangular - prism

Using the volume formula (V = l\times w\times h), for the bottom prism with (l_2 = 10\mathrm{cm}), (w_2 = 11\mathrm{cm}), (h_2 = 2\mathrm{cm}), we have (V_2=l_2\times w_2\times h_2=10\times11\times2 = 220\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=210+220 = 430\mathrm{cm}^3).

Answer:

430