This is a ratio problem; the ratio of the length to width is constant (and therefore equal):
4 /6 = 15 / x
Now, with a ratio, we may do any allowable algebra operation: cross-multiply, invert both sides, multiply or divide both sides by the same amount, etc.
Let's cross-multiply:
4x = (15)(6)
x = 90/4
x = 22.5 in.
Answer:
the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
Step-by-step explanation:
since the volume of a cylinder is
V= π*R²*L → L =V/ (π*R²)
the cost function is
Cost = cost of side material * side area + cost of top and bottom material * top and bottom area
C = a* 2*π*R*L + b* 2*π*R²
replacing the value of L
C = a* 2*π*R* V/ (π*R²) + b* 2*π*R² = a* 2*V/R + b* 2*π*R²
then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then
dC/dR = -2*a*V/R² + 4*π*b*R = 0
4*π*b*R = 2*a*V/R²
R³ = a*V/(2*π*b)
R= ∛( a*V/(2*π*b))
replacing values
R= ∛( a*V/(2*π*b)) = ∛(0.03$/cm² * 600 cm³ /(2*π* 0.05$/cm²) )= 3.85 cm
then
L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm
therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
Answer:
1.5
Step-by-step explanation:
picture
The lateral surface of a cylinder can be found with the equation
A = 2 π r h Substitute in your values.
A = 2 π (11) (7) Multiply 11 and 7.
A = 2 π (77) Multiply 77 and 2.
A = 154π Don't simplify anymore so you can keep pi in the answer.
The surface are uses the equation
A = 2 π r h + 2 π r² Substitute in your values.
A = 2 π (11) (7) + 2 π (11)² Simplify and multiply your terms.
A = 2 π (77) + 2 π (11)²
A = 154 π + 2 π (11)²
A = 154 π + 2 π (121)
A = 154 π + 242 π Since both terms are in terms of pi, you can combine them.
A = 396π Stop simplifying to leave the answer in terms of pi.
B because it is creating it
With would be 3.4
