Question

1. the diagram shows the dimensions, in centimeters, of tw prisms joined together. what is the combined volume of these prisms, in cubi a 24 cubic centimeters b. 48 cubic centimeters c. 96 cubic centimeters d. 144 cubic centimeters

Explanation:

Step1: Calculate the volume of the first prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). For the first prism, \(l = 3\mathrm{cm}\), \(w = 2\mathrm{cm}\), \(h = 8\mathrm{cm}\). So \(V_1=3\times2\times8 = 48\mathrm{cm}^3\)

Step2: Calculate the volume of the second prism

For the second prism, \(l = 4\mathrm{cm}\), \(w = 3\mathrm{cm}\), \(h = 4\mathrm{cm}\). Using the volume formula \(V = l\times w\times h\), we get \(V_2 = 4\times3\times4=48\mathrm{cm}^3\)

Step3: Calculate the combined volume

The combined volume \(V = V_1 + V_2\). Substitute \(V_1 = 48\mathrm{cm}^3\) and \(V_2 = 48\mathrm{cm}^3\) into the formula, \(V=48 + 48=96\mathrm{cm}^3\)

Answer:

C. 96 cubic centimeters