In the figure to the right, AE + DC = 1 1/5 cm, AB = 1 3/4 cm, DE = 1 1/4 cm, and BC = 1 3/10 cm. Find the perimeter of the figu
re.
1 answer:
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Answer:
Minimum dimensions are r=3cm, h=9cm
Minimum Cost=$254.47
Step-by-step explanation:
Volume of a Cylinder=πr²h
Volume of the Open Top Cylinder=81π cm³.
Therefore:
πr²h=81π
The bottom costs $3 per cm² and the side costs $1 per cm².
Total Surface Area of the open top Cylinder= πr²+2πrh
Cost, C=3πr²+2πrh
As the Volume is fixed.
πr²h=81π
r²h=81
h=81/r²
Modifying C,
We differentiate C with respect to r
C'=
At the minimum cost, C'=0.
Next we solve C'=0 for r
6πr³-162π=0
6πr³=162π
r³=27
r=3
The dimensions of the cylinder at minimum cost are therefore:
r=3 cm
h=81/9=9cm
The minimum cost of the Cylinder
C=3πr²+2πrh
=(3XπX3²)+(2XπX3X9)
=$254.47
<u>Given</u>:
Sammy can paint the house by himself in 15 hours. With Nolan's help, it only takes 9 hours.
We need to determine the time it would take for Nolan to paint the house by himself.
<u>Time taken by Nolan:</u>
Let the rate that Sammy can paint the house by himself is
The rate that Sammy and Nolan together paint the house is
To determine the rate that it takes for Nolan to paint the house by himself is to subtract the rates.
Thus, we have;
Thus, the rate that it would take Nolan to paint the house by himself is
The time that it takes for Nolan to paint the house by himself can be determined using the formula,
Substituting the values, we have;
Thus, Nolan takes 22.5 hours to paint the house by himself.