Question

A can in the shape of a right circular cylinder is required to have a volume of 700 cubic centimeters. The top and bottom are made up of a material that costs 8� per square centimeter, while the sides are made of material that costs 5� per square centimeter. Find a function that describes the total cost of the material as a function of the radius r of the cylinder

Answer 1

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 2

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