Dimensions 6130

The aquarium dimensions are in the ratio a: b: c = 5: 2: 4. 6609 cm² of glass was used for its production. How many liters of water will fit in the aquarium if it reaches 5 cm below its edge?

Correct answer:

V =  35.075 l

Step-by-step explanation:

$$\begin{gathered} S=6609/100=\frac{6609}{100}=66.09{\text{dm}}^2 \\ a:b:c=5:2:4 \\ a=5x \\ b=2x \\ c=4x \\ S=a\cdot b+2\cdot c\cdot (a+b) \\ 5x\ast 2x+2\ast 4x\ast (5x+2x)=66.09 \\ 5x\cdot 2x+2\cdot 4x\cdot (5x+2x)=66.09 \\ 66x^2-66.09=0 \\ a=66;b=0;c=-66.09 \\ D=b^2-4ac=0^2-4\cdot 66\cdot (-66.09)=17447.76 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{\pm \sqrt{17447.76}}{132} \\ {x}_{1,2}=\pm 1.0006815859021 \\ {x}_1=1.0006815859021 \\ {x}_2=-1.0006815859021 \\ \text{ Factored form of the equation: } \\ 66(x-1.0006815859021)(x+1.0006815859021)=0 \\ x=x_1=1.0007\doteq 1.0007 \\ a=5\cdot x=5\cdot 1.0007\doteq 5.0034\text{dm} \\ b=2\cdot x=2\cdot 1.0007\doteq 2.0014\text{dm} \\ c=4\cdot x=4\cdot 1.0007\doteq 4.0027\text{dm} \\ {c}_1=5/10=\frac{1}{2}=0.5\text{dm} \\ V=a\cdot b\cdot (c-c_1)=a\cdot b\cdot (c-\frac{1}{2})=5.0034\cdot 2.0014\cdot (4.0027-0.5)=35.075\text{l} \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example