1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
leonid [27]
3 years ago
6

Forty square inches of material is available to make a cylindrical; can of tuna and water. What dimensions of the can will give

the most volume?
Mathematics
1 answer:
krek1111 [17]3 years ago
3 0

The dimensions of the can are 1.457 inches and 2.913 inches that will give the most volume

Step-by-step explanation:

Let us revise the rule of surface area and volume of a cylinder

  • S.A = 2π r h + 2π r²
  • V = π r² h

Forty square inches of material is available to make a cylindrical; can of tuna and water, we need to find the dimensions of the can that will give the most volume

∵ S.A = 40 inches²

∵ S.A = 2π r h + 2π r²

∴ 2π r h + 2π r² = 40

Let us use this rule to find h in terms of r

- Subtract 2π r² from both sides

∵ 2π r h = 40 - 2 π r²

- Divide both sides by 2π r

∴ h=\frac{40-2\pi r^{2}}{2\pi r}

∴ h=\frac{40}{2\pi r}-\frac{2\pi r^{2}}{2\pi r}

∴ h=\frac{20}{\pi r}-r

∵ V = π r² h

- Substitute h by its value above

∴ V=\pi r^{2}(\frac{20}{\pi r}-r)

∴ V = 20 r - π r³

To find the most volume differentiate it with respect to r and equate it by 0 to find the value of r

∵ \frac{dV}{dr} = 20 - 3π r²

∵ \frac{dV}{dr} = 0

∴ 20 - 3π r² = 0

- Add 3π r² to both sides

∴ 20 = 3π r²

- Divide both sides by 3π

∴ r² = 2.122

- Take √ for both sides

∴ r = 1.457 inches

To find h substitute the value of r in the expression of h

∵ h=\frac{20}{\pi r}-r

∴ h=\frac{20}{\pi (1.457)}-(1.457)

∴ h = 2.913 inches

The dimensions of the can are 1.457 inches and 2.913 inches that will give the most volume

Learn more:

You can learn more about volume of solids in brainly.com/question/6443737

#LearnwithBrainly

You might be interested in
identify a horizontal or vertical stretch or compression of the function f(x)=x^2 by observing the equation of the function g(x)
Tanzania [10]
Dentify<span> a </span>horizontal<span> or </span>vertical stretch<span> or </span>compression<span> of the</span>function<span> ƒ(</span>x<span>) = x2 by </span>observing<span> the </span>equation<span> of the </span>function g(x) = (9x)2<span>. ... </span>2<span>Answers. 0 votes. Let </span>f<span> (</span>x<span> ) is a </span>function<span> and c be a positive real number, the graph of the </span>function g<span> (</span>x<span> ) = </span>f<span> (c</span>x<span> ) is represented as follows. when, c > 1, the </span>function<span> .</span>
8 0
3 years ago
A blouse originally $29..99 is 15% off. Marlene has a coupon for an additional
Svetllana [295]

Answer:

$19.45

Step-by-step explanation:

add the 15% to the 20%, which gives you 35%. Then, subtract 35% from 29.99, which gives you 19.45

8 0
2 years ago
Read 2 more answers
Start 14 . skip count by tens to 54 . do the ones digits change ? explain​
olya-2409 [2.1K]

Answer:

No because if you count by tens your basically only adding 1 each time to the tens place. 14, 24, 34, 44, 54. Each time you count by ten the only digit that changes is the tens place.

Step-by-step explanation:

7 0
3 years ago
Solve the equation 3/4(8b-4)=-2
Mademuasel [1]
1/6 is ur answer
hope i helped
3 0
3 years ago
Read 2 more answers
Lupe and her friends spent $20 on snack mix and water. They bought x bags of snack mix and y bottles of water. They bought a tot
Tresset [83]

Answer:

6 bags of snack mix

Step-by-step explanation:

x bags of snack mix

y bottles of water

The equations in the question is given as;

20.00 = 2.50x + 1.00y  (i)

11 = x + y (ii)

From eqn (ii);

11 - y = x

substitute the value of x in eqn (i);

20.00 = 2.50(11 - y) + 1.00y

20.00 = 27.5 - 2.50y + 1.00y

20.00  - 27.5  = - 1.50 y

- 7.5 = - 1.50 y

y = - 7.5 / (- 1.5) = 5

Since we are interested in the value of x. Substitute the value of y in eqn (ii);

11 = x + 5

x = 11 - 5 = 6

3 0
3 years ago
Other questions:
  • Ed is 7 years older than Ted. Ed’s age is also 3/4 times Ted’s age. How old are Ed and Ted?
    9·1 answer
  • 4a^2-9(x+y)^2 factories this step by step pls. Anyone !! Help me pls!!​
    12·1 answer
  • Solve for x. |2x - 8| &gt; 6
    10·2 answers
  • Solve for V:<br><br>V+9/15=0
    10·1 answer
  • If AB is parallel to CD and the slope of CD is-5, what is the slope of AB?
    15·1 answer
  • Write 480,000 in scientific notation.
    10·2 answers
  • Pls answer the question important
    13·2 answers
  • Xy and bd are parallel lines
    14·1 answer
  • What is the answer to C?
    15·1 answer
  • 14x=x^2-15<br><br> find the value of x
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!