30. A cylindrical diesel tank is 1.25 meters high and has a radius of 0.60 meter. If the tank can only be filled to an \( 85 \% \) capacity to allow for expansion of the fuel, what is the maximum volume of fuel? Round to the nearest hundredth. \( \begin{array}{ll}\text { A } 4.71 \mathrm{~m}^{3} & \text { C } 1.41 \mathrm{~m}^{3} \\ \text { B } 2.01 \mathrm{~m}^{3} & \text { D } 1.20 \mathrm{~m}^{3}\end{array} \)

To find the maximum volume of fuel in the cylindrical diesel tank, we first calculate the total volume of the cylinder using the formula: \[ V = \pi r^2 h \] Where \( r \) is the radius and \( h \) is the height. Plugging in the values: \[ V = \pi (0.60)^2 (1.25) \approx \pi (0.36)(1.25) \approx \pi (0.45) \approx 1.41 \, \text{m}^3\,. \] Now, since the tank can only be filled to \( 85\% \) capacity, we calculate: \[ \text{Max volume of fuel} = 1.41 \times 0.85 \approx 1.20 \, \text{m}^3. \] Therefore, the maximum volume of fuel is \( 1.20 \, \text{m}^3 \), corresponding to option D. Now, let's dive into some interesting tidbits related to this topic! Did you know that the concept of using cylindrical tanks for storage dates back to ancient civilizations? These cylindrical shapes are considered optimal for containing liquids because they minimize stress on the structure and maximize volume due to their geometric properties. Romans and ancient Greeks already understood this principle when they began using rounded containers! If you’re ever in a pinch while tackling similar volume calculations, remember to double-check your radius and height measurements! A common mistake is to confuse radius (the distance from the center to the edge) with diameter (the total width across the cylinder). Always verify which measurement you're using to avoid errors in calculating the volume!