Mike chose

Mike selected four identical cubes, three identical prisms, and two identical cylinders from a construction kit. Each cube has an edge length of 3 cm. Each prism has two dimensions the same as the cube, and its third dimension is twice as long. Each cylinder has a base diameter of 3 cm and a height equal to the edge of the cube.

What is the total volume of all these solids?

Final Answer:

V =  312.4115 cm³

Step-by-step explanation:

$$\begin{gathered} a=3\text{cm} \\ {V}_1=a^3=3^3=27{\text{cm}}^3 \\ {V}_2=a\cdot a\cdot (2\cdot a)=3\cdot 3\cdot (2\cdot 3)=54{\text{cm}}^3 \\ D=3\text{cm} \\ r=D/2=3/2=\frac{3}{2}=1.5\text{cm} \\ {V}_3=\pi \cdot r^2\cdot a=3.1416\cdot 1.5^2\cdot 3\doteq 21.2058{\text{cm}}^3 \\ V=4\cdot V_1+3\cdot V_2+2\cdot V_3=4\cdot 27+3\cdot 54+2\cdot 21.2058=312.4115{\text{cm}}^3 \end{gathered}$$

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