Question

6 m3 A ready mixed concrete tanker is to be constructed 4m from steel as a cylinder with conical ends. a) Calculate the total volume of concrete that can 1.8 mbe held in the tanker. b) How long would the tanker be if the endswere hemispheres instead of cones, but thecylindrical section remained the same? c) How much more or less concrete would fit in the tanker if the ends were hemispheres insteadof cones? d) Show that the surface area of the tanker:1 with conical ends is about 30 m2li with hemispherical ends is about 33 m². e) Overall, which do you think is the better design for the tanker? Give reasons for your answer.​

Answer 1

To calculate the total volume of concrete in the tanker, find the volume of the cylindrical section and conical ends. If the ends were hemispheres, the length of the tanker would be the same as the cylindrical section. Calculate the difference in volume between conical and hemispherical ends. Compare the surface area of the tanker with conical and hemispherical ends. Consider factors like cost, strength, and efficiency to determine the better design for the tanker.

Step-by-step explanation:

a) To calculate the total volume of concrete that can be held in the tanker, we need to find the volume of the cylindrical section and the volume of the conical ends. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height. The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. The total volume is the sum of the volume of the cylindrical section and the volume of the two conical ends. Let's calculate:

1. Volume of cylindrical section = (π × r^2 × h)
2. Volume of one conical end = (1/3) × (π × r^2 × h)
3. Total volume = Volume of cylindrical section + 2 × Volume of one conical end

b) If the ends were hemispheres instead of cones, the length of the tanker would be the same as the length of the cylindrical section, as the hemispheres would have the same radius as the cylinder.

c) To calculate the difference in volume, we need to compare the volume of the conical ends to the volume of the hemispherical ends. The volume of a hemisphere is given by the formula V = (2/3)πr^3. Let's calculate:

1. Volume of conical ends = 2 × (1/3) × (π × r^2 × h)
2. Volume of hemispherical ends = 2 × (2/3) × (π × r^3)
3. Difference in volume = Volume of hemispherical ends - Volume of conical ends

d) To calculate the surface area of the tanker, we need to find the areas of the cylindrical section and the conical ends. The surface area of a cylinder is given by the formula A = 2πrh + 2πr^2, where r is the radius and h is the height. The surface area of a cone is given by the formula A = πrl + πr^2, where r is the radius and l is the slant height. Let's calculate:

1. Surface area of cylindrical section = 2πrh
2. Surface area of one conical end = πrl + πr^2
3. Total surface area = Surface area of cylindrical section + 2 × Surface area of one conical end

e) To determine which design is better for the tanker, we need to consider factors such as cost, strength, and efficiency. The conical ends may provide better stability and distribute pressure more evenly, while the hemispherical ends may be easier to manufacture and maintain. It would also depend on the specific requirements and constraints of the tanker's use.