Question

a modern art museum has the dimensions shown in the figure.
what is the total amount of space inside the museum?
□ cubic meters

Explanation:

Step1: Calculate the volume of the larger prism

The formula for the volume of a prism is \(V = B\times h\), where \(B\) is the base area and \(h\) is the height. For the larger part, assume the base is a rectangle with length \(l = 10\space m\) and width \(w=12\space m\), and height \(h = 30\space m\). The base area \(B_1=10\times12 = 120\space m^{2}\). The volume \(V_1=B_1\times h=120\times30=3600\space m^{3}\)

Step2: Calculate the volume of the smaller triangular - prism part

The base of the smaller part is a triangle. The area of a triangle is \(A=\frac{1}{2}\times b\times h\), where \(b = 12\space m\) and \(h = 4\space m\). So \(B_2=\frac{1}{2}\times12\times4 = 24\space m^{2}\). The length (height of the prism) is \(l = 10\space m\). The volume \(V_2=B_2\times l=24\times10 = 240\space m^{3}\)

Step3: Calculate the total volume

The total volume \(V=V_1 + V_2\). Substitute \(V_1 = 3600\space m^{3}\) and \(V_2=240\space m^{3}\) into the formula. \(V=3600 + 240=3840\space m^{3}\)

Answer:

\(3840\)