Building blocks

Rosa bought a set of building blocks for her younger brother, Owen, for his birthday. Owen opened the gift and immediately used all 35 blocks in the set to build a tower shaped like a rectangular prism. Each block is a cube that is 1 1/2 inches along each edge.
What is the volume of Owen's tower?
Write your answer as a whole number, proper fraction, or mixed number.

Final Answer:

V =  118 ¹⁄₈ = 945/8 in³

Step-by-step explanation:

$$\begin{gathered} n=35 \\ a=1\frac{1}{2}=1+\frac{1}{2}=\frac{1\cdot 2+1}{2}=\frac{2+1}{2}=\frac{3}{2}=1.5\text{in} \\ {V}_1=a\cdot a\cdot a=\frac{3}{2}\cdot \frac{3}{2}\cdot \frac{3}{2}=\frac{27}{8}=3.375{\text{in}}^3 \\ V=n\cdot V_1=35\cdot \frac{27}{8}=\frac{35\cdot 27}{8}=\frac{945}{8}=\frac{945}{8}{\text{in}}^3=118\frac{1}{8}{\text{in}}^3=118.125{\text{in}}^3 \end{gathered}$$

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