Question

1. a platform like the one shown was built to hold a sculpture for an art exhibit. what is the volume of the figure? example 4

Explanation:

Step1: Calculate the volume of the top rectangular prism

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). For the top prism, \(l = 20\space m\), \(w = 8\space m\), \(h = 5\space m\). So \(V_1=20\times8\times5 = 800\space m^3\)

Step2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V=\pi r^2h\). Given \(r = 8\div2=4\space m\), \(h = 15\space m\). So \(V_2=\pi\times4^2\times15=240\pi\approx 240\times 3.14 = 753.6\space m^3\)

Step3: Calculate the volume of the bottom rectangular prism

Using the volume formula for a rectangular prism \(V = l\times w\times h\). For the bottom prism, \(l = 20\space m\), \(w = 8\space m\), \(h = 5\space m\). So \(V_3=20\times8\times5=800\space m^3\)

Step4: Calculate the total volume

The total volume \(V = V_1+V_2+V_3\). Substitute the values: \(V=800 + 753.6+800=2353.6\space m^3\)

Answer:

\(2353.6\space m^3\)