Question

what is the volume of this figure? 1 cm 3 cm 4 cm 5 cm 3 cm 1 cm 3 cm 4 cm cubic centimeters

Explanation:

Step1: Divide the figure into two rectangular - prisms

We can divide the L - shaped figure into two rectangular prisms. One prism has dimensions \(3\times1\times5\) and the other has dimensions \(3\times1\times4\).

Step2: Calculate the volume of the first prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). For the first prism with \(l = 3\mathrm{cm}\), \(w = 1\mathrm{cm}\), and \(h = 5\mathrm{cm}\), \(V_1=3\times1\times5 = 15\mathrm{cm}^3\).

Step3: Calculate the volume of the second prism

For the second prism with \(l = 3\mathrm{cm}\), \(w = 1\mathrm{cm}\), and \(h = 4\mathrm{cm}\), \(V_2=3\times1\times4=12\mathrm{cm}^3\).

Step4: Calculate the total volume

The total volume \(V = V_1 + V_2\). So \(V=15 + 12=27\mathrm{cm}^3\).

Answer:

27