Area is a quantity that expresses the extent of a two-dimensional or three-dimensional surface or shape.

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Area between a semicircle and a 45° line

I'm studying for a Calculus test and I met the following question: There's a semicircle $$y=\sqrt{1-x^2}$$ and a line at 45° degrees v=x. The task was to find the area in the positive quadrant. I ...
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0answers
15 views

Question about volume/area of cone and hemisphere [on hold]

Can any one answer this question? + i dont have any answers of it cz it came in my recent cie paper but still i am confused what could be the possible solution for this.
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0answers
17 views

Highest area rectangle in a rectangle trapezoid

There is a rectangle trapezoid with base sizes 8 and 24 and height of 12. Is there a way of finding highest area rectangle inside a trapezoid which 2 points would be in sides of a trapezoid? I ...
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6answers
460 views

Finding the largest triangle inscribed in the unit circle

Among all triangles inscribed in the unit circle, how can the one with the largest area be found?
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0answers
17 views

The area of a stereographic projection

I'm newbie at multidimensional integration and I'm trying to make a working algorithm in Wolfram that can help me compute the areas on the unit sphere without complicated parametrization, provided I ...
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1answer
25 views

Length of trapezoidal base and its maximum area in terms of “$d$”. [on hold]

(1)I need to find the length of the bottom base of a trapezoid if its area is to be a maximum? and (2)the maximum area of the trapezoid cross-section in terms if "$d$" (the diameter of a semicircle ...
2
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2answers
66 views

Curve fitting the cross sectional area of a cake.

For my final Calculus project I have to find the area of a Bundt cake through the use of cross sectional areas. (Cakeulus) While most seniors in High School who run into this popular calculus project ...
4
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0answers
49 views

Are closed simple curves with that property necessarily circles?

This is a more interesting follow-up to the question Are closed simple curves with this property necessarily circles? Let $\gamma:[0,1]\to \mathbb R^2 $ be a closed simple $C^1$ convex curve and ...
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1answer
50 views

Are closed simple curves with this property necessarily circles?

Let $\gamma:[0,1]\to \mathbb R^2 $ be a closed simple curve and $\Gamma$ be the region enclosed by $\gamma$. Let $O$ be the center of mass of $\Gamma$. Suppose that any line that goes through ...
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0answers
18 views

Given a set of points, find the plane parallel to plane $p$ where your plane cuts the area in half.

Given a set of point $G=\{(x,y,z) | 0 \le x\le2, 0 \le y \le 2, 0 \le z \le xy\}$ for all $x,y>0$ Find the plane $p$ parallel to plane $zy$ whereas you get two areas equal in size What I did was ...
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2answers
23 views

Derivation of second moment of area of a circle, a small question

I hope this question will be allowed on math.stackexchange, as the question is a mathematical one even though the subject might be from engineering. I am trying to derive the formula for the second ...
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1answer
24 views

Find the centroid of the region under the graph of the function $ w(x) = 4.5 + a x^{3} $ between $ x = 0 $ and $ x = 5 $. [closed]

I need to find the centroid to determine where the equivalent force is acting on the region under the graph of $ w $ between $ x = 0 $ and $ x = 5 $. The given information is $$ w(0) = 4.5 ~ ...
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3answers
51 views

If the surface area of a box is 32 and its volume is doubled what is the new surface area? [closed]

Original surface area :32 Original volume: x New volume: 2x What is the new surface area? Please provide an explanation or show work, I don't know how to do it.
4
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4answers
123 views

What is the area of shaded region which is lies between outer and inner circle.

There is a outer circle with radius 2r and another inner circle with radius r whose center is the middle of big circle.As depicted in the following figure. Foo graph Image There is a sector of 120 ...
0
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0answers
39 views

Finite region enclosed by two curves when $f(x)$ and $g(x)$ contain variable a

I need to find the area enclosed by the curves $f(x) = x^3 - ax$ and $g(x) = (a-1)x^2$. $a > 0 $ This I can do by subtracting the integral of the "lower function" from the integral of the "upper ...
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1answer
28 views

Find the area of the region in $X$-$Y$ plane: $\{(x,y) \in \mathbb{R}^2| x^2+y^2 \leq 144; \quad \sin(2x+3y) \leq0 \}$

$x^2+y^2=12^2$ is a circle having centre at $(0,0)$ & radius $12$. So,I could easily mark the first inequality. But $\sin(2x+3y)=0$ implies $2x+3y=n(\pi)$ where $n$ is any integer For $n=0$, ...
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5answers
89 views

Geometry - really hard trapezium problem.

Can anyone explain me how to find the area of this trapezium if we have a base and radius of the circle?
0
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1answer
47 views

Expected area of an internal triangle determined by a random point in a triangle

A point M is chosen at random (uniformly) inside an equilateral triangle ABC of area 1. How to find the expected area of the triangle ABM?
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1answer
36 views

Find area of solid using cylindrical shell method

Here's my problem, I have to use the shell method to find the area bounded between f(x)=4x-x^2 and y=3 by rotating about y=2. I understand I have to first solve for x. Which is weird because I have ...
0
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1answer
33 views

Square root of height of a paraboloid equal to radius?

I'm reading the book Mathematics: It's Content, Methods, and Meanings and I'm unsure as to how one of the variables in an example was derived. The question is about the volume of a paraboloid and here ...
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0answers
36 views

Find the area of a surface of revolution about the y-axis $x=\frac{y^3}{3}$ for $-2\leq y \leq 2$

I need to find the area of a surface of revolution about the y-axis for $x=\frac{y^3}{3}$ where $-2\leq y \leq 2$. I know that the formula for the area of a revolution surface about the x-axis on ...
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1answer
18 views

Compute a basic Side of two rooms, given total Area and total perimeter

My Gf's professor asked her to solve this problem: Two square rooms have an area of $52m^2$. The two rooms have a perimeter of 40 meters. Given this, we need to compute the length of the side of the ...
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1answer
61 views

The Area of shaded region in a circle

I'm having trouble solving this problem. I can't solve this. I don't know where and how to start. I don't know there is any formula for finding the area for this kind of shape, and if it did, I ...
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1answer
42 views

Relation between Areas

Given a quadrilateral $ABCDEF$, where $B$ is the midpoint of $\overline{AC}$ and $E$ is the midpoint of $\overline{FD}$, prove the relation $$a+d = c+b,$$ where $a$, $b$, $c$, $d$ denote the ...
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1answer
32 views

Area between two curves in terms of x

I am given two equations and a graph. The equations are $$x=-y^3+4y+9$$ $$x=y^2-5y$$ The problem shows a graph with a shaded region, and I am only to find the area above $y=-1$. I want to set up ...
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1answer
25 views

I have to find the surface area of a paraboloid within a cylinder.

I have to find the surface area of a paraboloid within a cylinder. The paraboloid is $x = y^2 + z^2$ and the cylinder is $y^2 + z^2 = 4$, and I know the equation but I have no idea how to set this ...
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0answers
28 views

Possible areas within an integer grid

Given a 1x1 grid with 4 lattice points $[(0,0),(0,1),(1,0),(1,1)]$ (equivalent to a $2 \times 2$ grid of vertices), there are 2 shapes and areas that can be formed: a triangle and a square. There are ...
2
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1answer
26 views

Evaluating area using an integral in polar coordinates

I am trying to find the area of a circle which is given by the polar parameterization $$r(\phi) = \cos\phi + \sin\phi.$$ I can evaluate it in 2 ways and don't know why I get different answers. First ...
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2answers
36 views

How do I prove that the area of a sphere is the least possible area for a given volume?

Or, why do soap bubbles have the shape of a sphere and not that of unicorns? What's the math behind it?
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2answers
35 views

Double integrals- cartesian to polar [closed]

$$\int^\infty_{-\infty}\int^\infty_{-\infty} \frac{1}{a^2 + x^2 +y^2}\,dy\,dx$$ How can I convert the integral to polar form the hint given in the question is:x-y plane
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1answer
41 views

Question regarding the area of a region

I was faced with the following problem, taken from my math textbook : Given the function $f(x)=x^2+6x+1$, find an approximation for the area encapsulated by the region $R(x,y)$ where $f(x)+f(y) \leq ...
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0answers
23 views

Area under parametrics that go through an interval more than once?

So say I have parametrics such as x=t^2 and y=t. This is a sideways parabola. Say I integrate with the parametric formula y(t)x'(t). What area does this give? The area bounded by the upper part of the ...
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3answers
19 views

Determine the area of ​​the shape bounded by the curves

$$y=x^2 + 1, x=2, x=1, y=0$$ I've got exam today and I'm learning how to solve this type of task. The exam is about derivations mostly.
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2answers
45 views

Calculating the area of an ellipse

I need to calculate the area of an ellipse described in polar coordinates by the following equation $$r=\frac{p}{1+\epsilon \cos{\theta}},\qquad |\epsilon| < 1$$ I need to so it by solving the ...
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1answer
22 views

Perimeter of equilateral triangle from its area

In an exercise, I have to answer the perimeter of a equilateral triangle knowing that its area is $$\sqrt{3}$$ How can I achieve it? I tried inventing equations, but all dead ends. Please explain.
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0answers
47 views

Area of an equilateral triangle

Prove that if triangle $\triangle RST$ is equilateral, then the area of $\triangle RST$ is $\sqrt{\frac34}$ times the square of the length of a side. My thoughts: Let $s$ be the length of $RT$. ...
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1answer
49 views

Use determinants to calculate the area bounded by 3 vectors

I have seen the proof of why the area of the parallelogram created by 2 vectors $u = \left(\begin{matrix} u_1\\ u_2 \end{matrix}\right)$ and $v = \left(\begin{matrix}v_1 \\ v_2 \end{matrix}\right)$ ...
2
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1answer
37 views

Area under the curve described by θ=ar

I'm interested in finding the area under the curve described by θ=ar, which is a linear curve with slope 'a' in polar coordinates. Here is what the curve looks like: ...
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0answers
41 views

What radius circle to remove from unit circle to make golden earring?

A circular lamina of radius $x$ is removed from a circular lamina of radius $1$. If the center of gravity is at the edge of the smaller circle (along the line connecting the two centers) what is $x$? ...
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1answer
38 views

Integration: Finding area, volume and arc length

I am new to integration, so please do not mark this question as "not enough research done" Here is the question (please open image in new tab to see it clearly) - I am getting stuck with the ...
2
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0answers
31 views

Perimeters Areas and Volumes

I have to write an article for a school magazine. I thought it is better to choose a simple topic like Perimeter, Area and Volume. I am looking for historical fact and surprising facts about ...
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0answers
46 views

Formula for area of circle made up of squares

I need to draw an approximate circle on a grid of squares and find its area. Each square must either be completely part of the circle or not at all occupied. Obviously, this means that it cannot be a ...
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1answer
21 views

Integration about x and y axes to find area

I have a problem statement that requires me to find area between the curves about x axis and about y axis. But my answers are not matching. Please find below my worked out solution - The ...
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2answers
653 views

Find the area of this irregular octagon inscribed in a circle [closed]

Find the area of the octagon pictured here I do have some ideas how to solve it, but do not want to write them down here, because I'm hoping to find some different approaches. Also, see 1978 ...
1
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1answer
27 views

Need Assistance with Calculating the Area of a Square when given the diagonal.

It's been several years since I've done this stuff---I'm trying to brush up for a Praxis exam in a few weeks. I've come across a problem I'm having a lot of trouble with. I'm given a square. The ...
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1answer
32 views

Calculate the area between functions

[I need to find the area between this three functions, therefore I need to use Integral g(x)-f(x) but I tried and it gives me negative and enormous numbers.]
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2answers
43 views

Calculating if a point is within the overlap of two circles

Two circles of equal radius (R) intersect as shown below. Assuming more points are uniformly distributed in an area with dimensions D*D, where D = 4*R. What is the probability that a point will be ...
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1answer
26 views

Finding $y=b$ that dissects the area between $ y=36, y=12, y=x^2$ into 2 equal halves.

Finding $y=b$ that dissects the area between $ y=36, y=12, y=x^2$ . what I did is solving the following equation: $\int_{0}^{6} 36-x^2\,dx$ - $\int_{0}^{\sqrt{b}} b-x^2\,dx$ = $\int_{0}^{\sqrt{b}} ...
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0answers
32 views

Area of circles on a wall

If you are painting a wall that is 10 ft by 12ft blue with gray polka dots on it, and the polka dots are spaced their diameter's distance away from each other at the shortest distance, how much paint ...
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1answer
40 views

How to find percentage of one rectangles area based on another rectangles area

I know I might sound the dumbest person in the galaxy, but I just wanted to make sure I am doing this right. I have a rectangle say [R1] placed inside a bigger rectangle [R2]. R1 will always be <= ...