For questions about area of plane figures.

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0answers
27 views

Sum of all n dimensional spheres?

I was messing around and made some code to find the area of an n dimensional sphere. I noticed that as n increases, the area tends towards zero. These were the results: ...
6
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1answer
54 views

How to calculate the area between $y=e^{-x}$, $y=x$ and $x=0$

My problem is that little point that comes from the equation $$e^{-x} = x$$ I can't solve that one. Is there another way without knowing that point or a way to calculate it? Thanks in advance!
0
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1answer
20 views

How to find the integration bounds when calculating area

To calculate an area between curves, I need to integrate with respect to x between the curve $y=\sqrt{2x}$, the x-axis and the line $y=\frac{4x-12}{5}$ My understanding, using google to display plot ...
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0answers
21 views

Surface area of cylindrical surface using double integrals

Please help lead me in the right direction for this question, I'll give a description of my progress so far. My understanding is that the formula for the surface area is given by this equation: ...
3
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1answer
42 views

Inequality between area and boundary length, $4\pi A \leq L^2 $

Suppose we have a simply connected region $R$ in $\mathbb{R}^2$ with area $A$ and the boundary of $R$ is a curve sufficiently well behaved (say piecewise $C^1$) that we can say it has length $L$. Then ...
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1answer
33 views

Calculate the viewing-angle on a square (3d-calc)

I'm in big trouble: My program (Java) successfully recognised a square drawn on a paper (by its 4 edges). Now I need to calculate, under which angle the webcam is facing this square. So I get the 4 ...
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1answer
28 views

ACDF (labelled clockwise) is a square of unit length. B is the midpoint of AC. E lies on FD such that FE = 1/4 and ED = 3/4. Find the area of BHEG.

I have solved this problem by use of the Cartesian plane, but the solution is long and I am sure that I have overkilled it and that there is a simpler solution... Based on where this question came ...
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1answer
34 views

Evaluate integral by interpreting it in terms of areas

I tried (a) and I got 5, but I am suppose to get a 4. I really need a good explanation to understand how to approach these problems. I tried searching in youtube and stuff, but it was not helpful. ...
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2answers
282 views
+50

$\pi$ in terms of $4$?

I'm trying to define $\pi$ in terms of $4$ by placing a unit circle inside a square, and subtracting the corners of the square. I'm attempting to use summation to define the area of a corner, then ...
0
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1answer
22 views

Elementary question: Integral of area function

I am sorry for this elementary question. I have searched a bit but haven't found what I am looking for precisely. I am trying to determine how to the volume of liquid in an irregularly shaped ...
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2answers
39 views

Prove that $\frac{1}{2}ab \equiv \int_0^b \! f(x) \, \mathrm{d}x$ when calculating the area of a right triangle.

Triangle $ABC$ is a right triangle with sides $AB$, $BC$ and $AC$. $a$ is the length of $AB$. $b$ is the length of $BC$. $c$ is the length of $AC$. If $a = 3$, and $b = 4$, we can use ...
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1answer
29 views

Find the area of the region enclosed by the curves in the first quadrant

Find the area of the region enclosed by the curves $y=3x^2$, $y=8x^2$, $4x+y=4$ in the first quadrant Do you start by finding the boundaries?
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1answer
30 views

Area of a region bounded by $y=\sqrt{|x|}$ and $5y = x+6$

Find the area of the region bounded by $y=\sqrt{|x|}$ and $5y = x+6$ by looking at where the curves intersected on a graph I got $$\int_{-1}^4\Bigg[\frac{x+6}{5} - \sqrt{|x|}\Bigg]\,\, dx + \int_4^9 ...
1
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0answers
33 views

How to calculate the height of a segment based on radius and area

I'd like to calculate the height of a segment based on the area. I have the radius of the circle, the area of the segment and need to calculate the height of the segment. I found the following ...
0
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1answer
28 views

How is the area of this triangle calculated

I was reading "Problems of Calculus in one variable" by I A MARON, and came across this solved example in first chapter which I am unable to comprehend, please help me understand this. Scan of the ...
0
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1answer
18 views

Area of ellipse formed by slicing a cylinder

What is the equation of the area of the ellipse when a cylinder of radius x is cut by a plane inclined at an angle a. Angle a is the angle between the plane and the axis of the cylinder. If a is 90 ...
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2answers
28 views

Find the area of a shaded region

I'm trying to teach myself some elements of calculus in preparation for my class next semester, but I'm not sure how to work this problem. I've always had trouble dealing with areas inside of shapes. ...
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1answer
13 views

Area of a Parallelogram Using Vectors

I am not sure if I am doing this problem correctly. I need to find the area of the parallelogram whose vertices are the points $P(0,1,1), Q(1,2,1), R(2,4,1), S(3,5,1)$ So to find the area I need to ...
0
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2answers
47 views

Surface are of a lightbulb

I have this picture: How could I calculate the area of a "thing" in red square? It is a circle.
4
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3answers
163 views

Triangles area question

This question came in RMO, an olympiad in India. I solved it but with the assumption that the lines are parallel, though we are not given this info in the question. In acute $\triangle ABC$, let D ...
2
votes
1answer
34 views

Find the Area Using Polar Coordinates and a Double Integral

Of the area inside the smaller loop of the equation $r = 1-2sin\theta$ Here's my attempt at a solution: The shape has an inner and an outer loop, both of which will terminate at the origin. ...
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1answer
17 views

What is the chance that a PDF with compact support is concave?

Relevant questions and answers, in chronological order: When do equations represent the same curve? Find a smooth function with prescribed moments Does a sequence of moments determine the function? ...
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2answers
72 views

Area+Pythagoras Theorem

In the figure below show that Area A + Area B = Area C. What is the answer to this question?
2
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1answer
27 views

Slice an ellipsoid into equally thick slices for maximal surface

After seeing a colleague slicing a nearly ellipsoid piece of ginger for his cup of tea into almost equally thick slices to get more surface area (so the tea would suck out the ginger taste better), i ...
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0answers
20 views

Calculating the Section of an Ellipse

Hi, I have been trying to make an interactive SVG web page with JavaScript that allows you to edit an ellipse and will calculate the area of 'pie' section based on the angles and dimensions you ...
0
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1answer
30 views

Estimate Area Under Graph

Estimate the area under the graph of f(x) = 6/x from x = 1 to x = 7 using 6 approximating rectangles and right endpoints. I keep getting 1 for delta x because (B-A)/N, and then I get values ...
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1answer
58 views

Area between $1$ and $2$ of $x^2$ and $x^{1/2}$ using integrals? [closed]

I need to find the area between $x = 1, x = 2$, between the functions $x^2$ and $x^{1/2}$. Please show all steps so I can get a better understanding! Thank you
0
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1answer
22 views

Area of a figure in terms of height and width

Attempting to give a thorough geometric answer to this question made me wonder: Can the area of any two-dimensional figure be expressed as a scaled product of its height and width? That is, for an ...
1
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1answer
30 views

Surface area of a conical frustum?

I was reading about a conical frustum on Wikipedia, but on Wikipedia does not include the proof of surface area of a conical frustum. How do we arrive at that formula?
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1answer
38 views

Can we find out the area of conical frustum by using triangles?

I have been trying to find out the area of conical frustum by using triangles.
0
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2answers
27 views

Innovation behind formula for surface area and volume of a sphere

When I saw some problems about innovation behind area of a circle in this site,I was wondering that about a sphere.we know volume of sphere is $\frac{4}{3}\pi*r^3$ and surface area is $4\pi*r^2$,but ...
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2answers
66 views

The probability that the sum of two random x y values from [0,10] is less than 13

Two numbers $x$ and $y$ are randomly selected between $0$ to $10$. Find the probability that their sum is less than $13$. I am scratching my head here trying to figure this out... Any help ...
0
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2answers
53 views

Indefinite integral with sector of ellipse

An ellipse is given by the following equation: $$ 152 x^2 - 300 x y + 150 y^2 - 42 x + 40 y + 3 = 0 $$ After solving for the midpoint we have: $$ 152 (x-1/2)^2 - 300 (x-1/2) (y-11/30) + 150 ...
55
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10answers
11k views

Is there a shape with infinite area but finite perimeter?

Is this really possible? Is there any other example of this other than the Koch Snowflake? If so can you prove that example to be true?
17
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6answers
343 views

Why is the area of the circle $πr^2$? [duplicate]

I searched many times about the cause of the circle area formula but I did not know anything so ... Why is the area of the circle $\pi r^2$? Thanks for all here.
1
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1answer
38 views

Area of Triangle

The position vectors of $A$ $B$ and $C$ relative to an origin $O$ are given by $OA=(2,1,3)$ $OB=(0,-1,7)$ and $OC=(2,4,7)$ Part i) Show that angle $BAC= \cos^{-1}(\frac{1}{3})$ Part ii) Using the ...
2
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1answer
50 views

Prove that every trapezoid and every parallelogram is measurable and derive the usual formulas for their areas

My question is from Apostol's Vol. 1 One-variable calculus with introduction to linear algebra textbook. Page 60. Exercise 3. Prove that every trapezoid and every parallelogram is measurable and ...
3
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3answers
156 views

Integrals and area of circle

I have no idea where to start this one guys: Write a definite integral whose value is the area of the region between the two circles: $$x^2+y^2=1$$ $$(x-1)^2+y^2=1$$ Do I need to find my ...
0
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1answer
26 views

Equation, Area and Circumference of A circle given equation of the tangent and center

I don't know how to solve for the Area and Circumference but I know how to solve for the equation but I just wanted to make sure... Any help and explanations would be appreciated :) Problem: A circle ...
0
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2answers
38 views

A measure of the surface area of the intersection of a sphere with a cone

I will be as detailed as possible on the problem. Think of the following. Take the unit hypersphere $S=\{x\in\mathbb{R}^p: \Vert x\Vert_2=1\}$. I have a matrix $M$ of size $n\times p$ with $n\leq p$ ...
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0answers
18 views

How do I determine for given two rectangles A & B, with B having constant dimensions, that B is more than 50% inside A? [duplicate]

I have 2 rectangles in a 2D plane, only in the first quadrant with limit 2000 x 2000: A (black) & B (red) Look at the attached image Both can change positions (coordinates, X & Y). B has ...
0
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0answers
22 views

why this formula doesn't work?

L=integral from theta(start) to theta (end) r d(theta )......to find the arc length we usually use L= integral from theta(start) to theta (end) sqrt r^2+(dr/dtheta)^2 dtheta why the first formula ...
0
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1answer
36 views

How is the area of a set of points in $\Bbb R^2$ defined?

Let $S$ be a subset of $\Bbb R^2$. If no vertical slice of $S$ contains gaps, we could define the area of $S$ through the following. $$A(S) = \int_{-\infty}^\infty\left(\sup\{y\in\Bbb R\mid (x,y)\in ...
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0answers
30 views

Area swept out by non-solar focus not same over equal time?

Per Kepler's laws, the area swept out by a line between the sun and a planet is equal for a given period of time. The sun is also one focus of the planet's elliptical orbit. What about the area swept ...
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1answer
13 views

Dealing with negative areas— coordinate geometry

Question: Find the area of a quadrilateral in the Cartesian plane, whose vertices are (-4, 5), (0, 7), (5, -5) and (-4, -2) My solution: [I meant to draw ...
2
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0answers
41 views

Is there a formula for calculating the area of 2d shapes on a sphere?

Let's say I have 8 90° triangles on a sphere, like this, where all the angles are 90° when measured: I know that the area of one of those triangles will be (4πr2) * 1/8 as each triangle will take ...
0
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2answers
23 views

Question on volume of swimming pool

Swimming pool is of length 20m, wide 5m and height of the swimming pool increase from the 1.6m to 4.4m. What is the volume of swimming pool? How I approached: Area of swimming pool = Area of cube + ...
0
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3answers
53 views

surface area of the solid (column side)

I made a problem But I'm stuck in solving .. :-( the problem is following. Find the surface area of the solid that lies under the paraboloid $z =x^2 + y^2$, above the $xy$-plane, ...
3
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2answers
121 views

Finding the area of a implicit relation

Let's say we have the function: $$x^2+y^2+\sin(4x)+\sin(4y)=4$$ I haven't taken Calculus III, in fact I'm just taking Calculus I. Since I learned how to find the derivative of implicit relations I ...
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1answer
27 views

Solving for surface area of a cylinder.

I am doing an online course and I have to solve for the surface area of a cylinder, the Volume is give and I must find the most efficient cylinder, the cylinder with the least surface area, an ...