Question

what is the volume of this figure? 2 cm 8 cm 1 cm 2 cm 5 cm 4 cm cubic centimeters

Explanation:

Step1: Divide the figure into two rectangular - prisms

The larger rectangular - prism has dimensions \(8\ cm\times2\ cm\times5\ cm\), and the smaller one has dimensions \(4\ cm\times1\ cm\times2\ cm\).

Step2: Calculate the volume of the larger rectangular - prism

The volume formula for a rectangular - prism is \(V = l\times w\times h\). For the larger prism, \(l = 8\ cm\), \(w = 2\ cm\), \(h = 5\ cm\), so \(V_1=8\times2\times5 = 80\ cm^3\).

Step3: Calculate the volume of the smaller rectangular - prism

For the smaller prism, \(l = 4\ cm\), \(w = 1\ cm\), \(h = 2\ cm\), so \(V_2 = 4\times1\times2=8\ cm^3\).

Step4: Calculate the total volume of the figure

The total volume \(V = V_1 + V_2\). So \(V=80 + 8=88\ cm^3\).

Answer:

88