All questions with tag [math: area]


Why does the cylinder with minimum surface area have a height equal to its diameter?

I'm attempting to recognize regarding why, with an offered volume, the size and also elevation of a cyndrical tube demand to be the very same for the minimum surface. This thread, demonstrates how to acquire the minimum surface of a cyndrical tube with an offered volume, yet does not clarify why this is.
2022-07-24 06:34:00

How to calculate the area of a 3D triangle?

I have works with of 3d triangular and also I require to compute its area. I recognize just how to do it in 2D, yet do not recognize just how to compute area in 3d. I have actually created information as adheres to. (119.91227722167969, 122.7717056274414, 39.3568115234375), (119.8951187133789, 122.7717056274414, 39.38057327270508), (121.119415...
2022-07-17 14:17:07

Optimization with cylinder

I have no suggestion just how to do this trouble in all. A round can without a top is made to have V cm^3 of fluid. Locate the measurements that will certainly decrease the price of the steel to make the canister. Given that no details volume is offered the tiniest quantity of steel for the can would certainly be absolutely no, which would cer...
2022-07-16 14:03:04

Why determinant of a 2 by 2 matrix is the area of a parallelogram?

Let $A=\begin{bmatrix}a & b\\ c & d\end{bmatrix}$. Just how could we show that $ad-bc$ is the area of a parallelogram with vertices $(0, 0),\ (a, b),\ (c, d),\ (a+b, c+d)$? Are the locations of the adhering to parallelograms the very same? $(1)$ parallelogram with vertices $(0, 0),\ (a, b),\ (c, d),\ (a+c, b+d)$. $(2)$ parall...
2022-06-06 09:33:13

Bath towel on the rope: minimize the area of self-intersection of a folded rectangle

This inquiry is connected to my bathroom towel, which I hold on a rope, so allow is enjoy (you can utilize your very own towel to do this experiment in bathroom - o). There is this rectangular shape with sides $a<b$. The rectangular shape is curved along a line that travels through the facility of the rectangular shape. At which angle $\...
2022-06-05 09:57:16

Areas versus volumes of revolution: why does the area require approximation by a cone?

Intend we revolve the chart of $y = f(x)$ concerning the $x$ - axis from $a$ to $b$. After that (making use of the disk method) the volume is $$\int_a^b \pi f(x)^2 dx$$ given that we approximate a little item as a cyndrical tube. Nonetheless, if we intend to locate the surface, after that we approximate it as component of a cone and also the for...
2019-05-18 16:43:11

Why is the derivative of a circle's area its perimeter (and similarly for spheres)?

When set apart relative to $r$, the by-product of $\pi r^2$ is $2 \pi r$, which is the area of a circle. In a similar way, when the formula for a round's quantity $\frac{4}{3} \pi r^3$ is set apart relative to $r$, we get $4 \pi r^2$. Is this simply a coincidence, or exists some deep description for why we should anticipate this?
2019-05-06 22:51:02

Why does area differentiate to perimeter for circles and not for squares?

I read this question a few days ago and also it obtained me assuming: the area of a circle is $\pi r^2$, which sets apart to $2 \pi r$, which is simply the border of the circle. Why does not the very same point take place for squares? If we start with the area formula for squares, $l^2$, this sets apart to $2l$ which is type of right yet jus...
2019-05-06 08:41:45