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3 years ago

Estimate by rounding to the nearest hundred 657 - 125.

Mathematics

1 answer:

DIA [1.3K]3 years ago

6 0

Answer:

700-100=600

Step-by-step explanation:

600

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A rectangular solid with a square base has a volume of 2,744 cubic inches. (Let w represent the length of the sides of the squar

vaieri [72.5K]

Answer:

For minimum surface area, the base length and height are equal in length and <u>equal to 14 inches.</u>

Step-by-step explanation:

Given:

Volume of rectangular solid (V) = 2744 cubic inches

Length of base side = 'w'

Height of solid = 'h'

We know that,

Volume = Area of base × Height

$2744=(w\times w)\times h\\\\2744=w^2h\\\\h=\frac{2744}{w^2}-----(1)$

Now, surface area of the solid is given as:

$Surface\ area=2\times (base\ area)+4(hw)\\\\Surface\ area=2w^2+4hw$

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$Surface\ area=2w^2+4\times\frac{2744w}{w^2}\\\\Surface\ area=2(w^2+\frac{5488}{w})$

Now, for minimum surface area, the derivative of surface area with respect to length 'w' must be 0.

Differentiating both sides with respect to 'w' and equating it to 0, we get:

$\frac{dS}{dw}=0\\\\\frac{d}{dw}[2(w^2+\frac{5488}{w})]=0\\\\2w-\frac{5488}{w^2}=0\\\\2w=\frac{5488}{w^2}\\\\w^3=\frac{5488}{2}\\\\w=\sqrt[3]{2744}= 14\ in$

Therefore, the base length is 14 inches.

Now, from equation (1), the height is given as:

$h=\frac{2744}{w^2}\\\\h=\frac{2744}{14^2}=14\ in$

Therefore, for minimum surface area, the base length and height are equal in length and equal to 14 inches.

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