Respuesta :
Answer:
the cost function is Cost=7000 m*$ /R + 50.265 $/m² * R²
Step-by-step explanation:
then the cost function is
Cost= cost of side area+ cost of top + cost of bottom = 2*π*R*L * 5$/m² +
π*R² * 8$/m² + π*R² * 8$/m²
since the volume V is
V=π*R²*L → V/(π*R²)=L
then
Cost=2*π*R*V/(π*R²) * 5$/m² + π*R² * 8$/m² + π*R² * 8$/m²
replacing values
Cost=2*700 m³ /R * 5$/m² + π*R² * 16$/m² = 7000 m*$ /R + 50.265 $/m² * R²
thus the cost function is
Cost=7000 m*$ /R + 50.265 $/m² * R²
Answer: 50.24r² + 7000/r
Step-by-step explanation:
The formula for determining the volume of a cylinder is expressed as
Volume = πr²h
Since the volume of the can is 700cm³, then
πr²h = 700
h = 700/πr²
The formula for determining the total surface area of a cylinder is expressed as
Total surface area = 2πr² + 2πrh
The surface area of the top and bottom of the can is 2πr².
Since top and bottom are made up of a material that costs $8 per square centimeter, then the cost is
2πr² × 8 = 16πr²
Since π = 3.14, the surface area of the top and bottom of the cylindrical can is
16 × 3.14 × r² = 50.24r²
The surface area of the side of the can is
2πrh = 2πr × 700/πr²
= 1400/r
Since the the sides are made of material that costs $5 per square centimeter, then the cost is
1400/r × 5 = 7000/r
The total cost of the material as a function of the radius, r of the cylinder is
50.24r² + 7000/r
