Question

b. find the volume of each figure to the nearest cubic unit.
4.
5.
6.

Explanation:

4.

Step1: Calculate the volume of the lower prism

The lower prism has length \(l = 5\), width \(w=4\), height \(h = 3\). The volume formula for a rectangular prism is \(V=l\times w\times h\).
\(V_1=5\times4\times3=60\)

Step2: Calculate the volume of the upper prism

The upper prism has length \(l = 5\), width \(w=(5 - 2)=3\), height \(h=(3 - 1)=2\). Using the volume formula \(V=l\times w\times h\)
\(V_2 = 5\times3\times2=30\)

Step3: Calculate the total volume

The total volume \(V = V_1+V_2\)
\(V=60 + 30=90\)

Step1: Calculate the volume of the rectangular - prism base

The base of the rectangular - prism has length \(l = 7\), width \(w = 7\), height \(h=3\). Using the formula \(V=l\times w\times h\)
\(V_1=7\times7\times3=147\)

Step2: Calculate the volume of the pyramid

The base area of the pyramid \(B = 7\times7 = 49\), height of the pyramid \(H = 8\). The volume formula for a pyramid is \(V=\frac{1}{3}BH\)
\(V_2=\frac{1}{3}\times49\times8=\frac{392}{3}\approx130.67\)

Step3: Calculate the total volume

The total volume \(V=V_1 + V_2\)
\(V=147+\frac{392}{3}=\frac{441 + 392}{3}=\frac{833}{3}\approx278\)

Step1: Calculate the volume of the rectangular - prism base

The rectangular - prism has length \(l = 11\), width \(w = 11\), height \(h = 2\). Using the formula \(V=l\times w\times h\)
\(V_1=11\times11\times2=242\)

Step2: Calculate the volume of the cylinder

The radius of the cylinder \(r=\frac{10}{2}=5\), height \(h = 2\). The volume formula for a cylinder is \(V=\pi r^{2}h\)
\(V_2=\pi\times5^{2}\times2=50\pi\approx157.08\)

Step3: Calculate the total volume

The total volume \(V=V_1+V_2\)
\(V=242 + 157.08=399.08\approx400\)

Answer:

\(90\)

5.