Question

what is the volume of the composite figure shown? 2,880 mm³ 1,008 mm³ 2,412 mm³ 3,465 mm³

Explanation:

Step1: Calculate the volume of the first rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). For the first prism (the taller one), \(l = 13\space mm\), \(w=12\space mm\), \(h=(15 - 3)=12\space mm\). So \(V_1=13\times12\times12\)

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Step2: Calculate the volume of the second rectangular prism

For the second prism (the shorter one), \(l=(15 - 13)=2\space mm\), \(w = 12\space mm\), \(h = 3\space mm\). So \(V_2=15\times12\times3\)

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Step3: Calculate the total volume

The total volume \(V = V_1+V_2\). So \(V=1872 + 1008\)

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Answer:

\(2880\space mm^{3}\)