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2 years ago

Slice of cake, height 7cm width 20cm need to find volume

1 answer:

3 0

Volume is length times width times height. So you should give 3 numbers to multiply they gave you 2. You probably copied the question wrong?

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

5 0

2 years ago

Plz help! Convert 6/9 into fractions with a denominater of 27 A. 6/7 B.21/27 C. 9/27 D.18/27

givi [52]

D. 6 x 3 = 18 and 9 x 3 = 27, hope this helps :)

8 0

2 years ago

Price of 50 kg rice rupees 7650 find the price of 1 kg rice

Lilit [14]

Answer:

price of 50 kg rice rupees 7650 find the price of 1 kg rice

so 50kg: 7650r

divide both sides by 50 to get 1

1kg=153 rupees

5 0

2 years ago

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Adele has 3 64-ounce cartons of orange juice and 3 48-ounce cans of apple juice. How much juice does she have altogether?

ale4655 [162]

I think if u add 364+348 you will get 712

4 0

2 years ago

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X + 34 = 40 what does "x" equal? explain

butalik [34]

Hey there!

6 + 34 = 40

so x = 6

Hope this helps
Have a great day (:

8 0

3 years ago

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