Indoor aquarium

World's biggest indoor aquarium. In its enormous tank with the capacity represented by the following polynomial V=4x³+43x²+63x

The aquarium is rectangular prism shape. Find the following:

1. If the aquarium's height is x, then find the area of the base (B).

2. Based on your results in (q1), find the width of the aquarium given that the length is l=(x+9)

3. If the height h = 11m, find the volume of the aquarium

Correct answer:

B = 4x^2+43x+63
w = 4x+9
V =  11220 m³

Step-by-step explanation:

$$\begin{gathered} V=4x^3+43x^2+63x \\ V=B\cdot x \\ B=V/x \\ B=4x^2+43x+63 \end{gathered}$$

$$\begin{gathered} l=x+9 \\ B=w\cdot l \\ w=B/l \\ w=4x+9 \end{gathered}$$

$$\begin{gathered} h=11\text{m} \\ x=h=11\text{m} \\ V=4\cdot x^3+43\cdot x^2+63\cdot x=4\cdot 11^3+43\cdot 11^2+63\cdot 11=11220{\text{m}}^3 \end{gathered}$$

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