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3 years ago

Help me with this one

Mathematics

1 answer:

solong [7]3 years ago

8 0

Answer:

64/88, 66/88, 55/88

Step-by-step explanation:

8/11, 3/4, 5/8

LCM = 88

8/11 = 8×8/11×8 = 64/88

3/4 = 3×22/4×22 = 66/88

5/8 = 5×11/8×11 = 55/88

Therefore:

8/11 = 64/88

3/4 = 66/88

5/8 = 55/88

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Step-by-step explanation:

From the information given:

The volume V of a closed cylindrical container with its surface area can be expressed as follows:

$V = \pi r^2 h$

$S = 2 \pi rh + 2 \pi r^2$

Given that Volume V = 250 in²

Then;

$\pi r^2h = 250 \\ \\ h = \dfrac{250}{\pi r^2}$

We also know that the cylinder contains top and bottom circle and the area is equal to πr²,

Hence, if we incorporate these areas in the total area of the cylinder.

Then;

$S = 2\pi r h + 2 \pi r ^2$

$S = 2\pi r (\dfrac{250}{\pi r^2}) + 2 \pi r ^2$

$S = \dfrac{500}{r} + 2 \pi r ^2$

To find the minimum by determining the radius at which the surface by using the first-order derivative.

$S' = 0$

$- \dfrac{500}{r^2} + 4 \pi r = 0$

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$r^3 = 39.789$

$r =\sqrt[3]{39.789}$

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Using the second-order derivative of S to determine the area is maximum or minimum at the radius, we have:

$S'' = - \dfrac{500(-2)}{r^3}+ 4 \pi$

$S'' = \dfrac{1000}{r^3}+ 4 \pi$

Thus, the minimum surface area will be used because the second-derivative shows that the area function is higher than zero.

Thus, from $h = \dfrac{250}{\pi r^2}$

$h = \dfrac{250}{\pi (3.414) ^2}$

h = 6.8275 in

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