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3 years ago

What is the volume of a rectangular prism with length equal to 13,width equal to 6 and height equal to 4

Mathematics

1 answer:

diamong [38]3 years ago

8 0

Given:

Length of the rectangular prism = 13 units.

Width of the rectangular prism = 6 units.

Height of the rectangular prism = 4 units.

To find:

The volume of the rectangular prism.

Solution:

We know that the volume of the rectangular prism is:

$V=l\times b\times h$

Where, l is length, b is breadth or width and h is the height of the rectangular prism.

Putting $l=13,b=6,h=4$ in the above formula, we get

$V=13\times 6\times 4$

$V=312$

Therefore, the volume of the given rectangular prism is 312 cubic units.

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Recall that the surface area of a cylinder is given by:

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$\displaystyle \begin{aligned} (0) &= 4\pi r - \frac{600}{r^2} \\ \\ 4\pi r - \frac{600}{r^2} &= 0 \\ \\ 4\pi r^3 - 600 &= 0 \\ \\ \pi r^3 &= 150 \\ \\ r &= \sqrt[3]{\frac{150}{\pi}} \approx 3.628\text{ cm}\end{aligned}$

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Then the height will be:

$\displaystyle \begin{aligned} h&= \frac{300}{\pi\left( \sqrt[3]{\dfrac{150}{\pi}}\right)^2} \\ \\ &= \frac{60}{\pi \sqrt[3]{\dfrac{180}{\pi^2}}}\approx 7.25 6\text{ cm} \end{aligned}$

In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.

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