A new company uses cylindrical gas tanks to deliver propane gas. As their orders increase, they switch to new gas tanks with triple the height and triple the radius of the original tanks. What will be the effect of the scaled dimensions on the volume of the tanks? A. The volume of the new tanks will be 81 times the volume of the original tanks. B. The volume of the new tanks will be 3 times the volume of the original tanks. C. The volume of the new tanks will be 9 times the volume of the original tanks. D. The volume of the new tanks will be 27 times the volume of the original tanks.

A ratio shows us the number of times a number contains another number. The correct option is D, The volume of the new tank is 27 times the volume of the original tank.

What is a Ratio?

A ratio shows us the number of times a number contains another number.

Let the height and the radius of the cylindrical gas tank be h units and r units.

The volume of the tank with a radius r units and height h units can be written as,

The volume of the original tank, V = πr²h unit³

Now, they switch to new gas tanks with triple the height and triple the radius of the original tanks. Therefore, the new height and the radius of the tank will be 3h units and 3r units.

Thus, The volume of the new tank with a radius of 3r units and height 3h units can be written as,

The volume of the new tank, V₁ = π(3r)²(3h) unit³

= 27 πr²h unit³

Furthermore, it take the ratio of the original volume and the new volume, we will get,

V / V₁ = πr²h unit³ / 27 πr²h unit³

V / V₁ = 1 /27

V₁ = 27V

Hence, the volume of the new tank is 27 times the volume of the original tank.

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