An aluminum can is to be constructed to contain 2400 cm3 of liquid. Let r and h be the radius of the base and the height of the can respectively. Find the radius of the base (r) and height of the can (h) that will minimize the amount of materials necessary to construct the can. The volume of a cylinder is given by V = Tr2h and the surface area is A = 2rrh + 27r?.

Question

Can you help me find the value of r and h? 

An aluminum can is to be constructed to contain 2400 cm3 of liquid.
Let r and h be the radius of the base and the height of the can respectively.
Find the radius of the base (r) and height of the can (h) that will minimize the amount of materials necessary to construct the can. The
volume of a cylinder is given by V = Tr2h and the surface area is A = 2rrh + 27r?.
Expand
Transcribed Image Text

An aluminum can is to be constructed to contain 2400 cm3 of liquid. Let r and h be the radius of the base and the height of the can respectively. Find the radius of the base (r) and height of the can (h) that will minimize the amount of materials necessary to construct the can. The volume of a cylinder is given by V = Tr2h and the surface area is A = 2rrh + 27r?.

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Applications of Derivative

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: y to 6. 2.

A: Click to see the answer

Q: Using the Integral Test, check the convergence of the following series by verifying the necessary co...

A: Integral test:   If f is continuous, positive, and decreasing on [1,∞)                 such that an ...

Q: Let f(x) = ax3 + bx2 +c, where a, b,c € R. The graph of f passes through thepoint (2,9). The graph o...

A: Click to see the answer

Q: Suppose that g (x) is a function that is defined and differentiable for all real numbers x and that ...

A: According to your question, a format of equation what I derived is attached but parallel you have to...

Q: need help solving problem

A: Click to see the answer

Q: Find k so that f has a relative extremum at the point where x = 3. k 2.

A: Click to see the answer

Q: Please show all work so that i may understand your answer, thank you for your time!

A: Click to see the answer

Q: need help solving problem

A: Given: sint=45  

Q: B 12 20 und cos(B)

A: Click to see the answer

Q: Can you help me find C"(3) ?

A: Given cost function, Cx=3000x8x2+5x-6

Q: Find the zeros of the polynomial function and state the multiplicity of each. f(x) = 3x-x-147x+ 49 T...

A: Click to see the answer

Q: Find the sum: - 4+ - 6+ - 8+ ... + – 10 Answer:

A: Given, The series -4 + (-6) + (-8) + ... +(-10).   To find: The sum -4 + (-6) + (-8) + ... +(-10).

Q: Find an equation of the tangent line to the graph of the function at the given point. y = 4 – x² – I...

A: Click to see the answer

Q: Please help me with this problem. Thank you!

A: Click to see the answer

Q: Find a polynomial function P, with real coefficients, that has the indicated zeros and satisfies the...

A: Click to see the answer

Q: Convert from rectangular to polar coordinates: Note: Choose r and 0 such that r is nonnegative and 0...

A: Click to see the answer

Q: A bicyclist traveled a distance of d=48.2 miles for t=3.7 hours at a constant rate. Use the formula ...

A: Click to see the answer

Q: Integrals of cot x and csc x Prove that  ∫ csc x dx = -ln | csc x + cot x | + C.

A: Click to see the answer

Q: A parking lot charges 3 dollars for the first hour (or part of an hour) and 2 dollars for each succe...

A: (a) Graph the function as shown below:

Q: A skydiver jumps from an airplane. Suppose that the distance she falls during the first t seconds be...

A: The distance she falls during the first t seconds before her parachute opens is s(t) = 976 (0.835t– ...

Q: For this week's discussion, you are asked to generate a continuous and differentiable function f(x) ...

A: Click to see the answer

Q: Suppose the demand function for a product is given by the function: D(g) 0.01g + 46 - Find the Consu...

A: Click to see the answer

Q: Find a polynomial function of smallest degree with integer coefficients that has the given zeros. 6...

A: Here given as 6 + 5i, 6 − 5i, 2, 4, 6 are roots of a polynomial function then px=x-6+5ix-6-5ix-2x-4x...

Q: A 25-year old woman burns 300 – 40t cal/hr while walking on her treadmill. Her caloric intake from d...

A: Click to see the answer

Q: Use the indicated substitution to evaluate the integral. 42csc (7x)cot (7x)dx, u=7x 42csc (7x)cot (7...

A: Click to see the answer

Q: Use any method to find the relative extrema of the function f (x) = 30x + 31xa. If there is no relat...

A: f(x)=30x+31x131 To Find: relative maximum and minimum

Q: ht) A curve with polar equation 9 r = 7 sin 0 + 36 cos 0 ents a line. This line has a Cartesian equa...

A: Click to see the answer

Q: Please show all work so that i may understand your answer, thank you for your time!

A: Click to see the answer

Q: Find the zeros of the polynomial function, and state the multiplicity of each. f(x) =x°(x- 3) (x+6) ...

A: Click to see the answer

Q: Find the center of mass of the given system of point masses mi        3         1          7 (xi,yi)...

A: Click to see the answer