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Katherine has a fish tank shaped like a triangular prism in her living room. The triangle that forms the base of the tank has a base of 24 inches and a height of 20 inches. The entire tank is 36 inches tall. What volume of water is needed to fill the tank if the tank is only filled to 6 inches below the top?

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MrRoyal

Answer:

[tex]Volume = 7200in^3[/tex]

Step-by-step explanation:

Given

[tex]B = 24[/tex] --- base of the tank base

[tex]h = 20[/tex] --- height of the tank base

[tex]H = 36[/tex] --- height of the tank

Required:

Determine the volume of water needed for 6 inches below the top

First, calculate the area of the tank base.

[tex]Area = \frac{1}{2}Bh[/tex]

[tex]Area = \frac{1}{2}*24*20[/tex]

[tex]Area = 12*20[/tex]

[tex]Area = 240[/tex]

If the tank is filled 6 inches below the top, this means that the height of the water is H - 6.

So, the volume is:

[tex]Volume = Area * (H - 6)[/tex]

Substitute 240 for Area and 36 for H

[tex]Volume = 240 * (36 - 6)[/tex]

[tex]Volume = 240 * 30[/tex]

[tex]Volume = 7200in^3[/tex]

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