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Questions tagged [area]

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

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Maximization problems

I am in a introductory course of calculus in several variables and i have these problems. A farmer wants to build a corral with pentagonal form(not regular) that is formed by the union of a rectangle ...
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using partial derivations to get the approximate error for this problem

The area of a triangle is $A=\frac{1}{2}a*b*sin(c)$ $𝑎*𝑏* sin( 𝑐)$, where $a$, $b$ are two sides of the triangle and $c$ is the included angle. In surveying a triangular plot of land, $a$ and $b$ ...
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Estimating Area Exam Question

Pieces of turf are 1m long by 0.5m wide. Each piece costs £3.79 . $1 * 0.5 = 0.5\text m^2$ a)Estimate the cost of turf required to cover these spaces. i) 9.6m by 2.4m $10 * 2 = 20\text m^2$ ...
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Calculate area enclosed by 4 curves

I am trying to find the area enclosed by 4 piecewise smooth curves. As can be seen from the figure, BLACK curve is a segment of a circle, C ...
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Definite integral of $1/(2\sin^4x + 3\cos^2x)$

I have $f = \frac 1 {(2\sin^4x + 3\cos^2x)}$ which area should be calculated from $0$ to $\frac{3\pi}2$. I noticed that $$\int_0^{\frac{3\pi}2} f \,dx= 3\int_0^{\frac{\pi}2} f \,dx$$ I tried to ...
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Calculating how much light gets through steel mesh (commonly used to make cages)

I have expanded steel mesh that I use to make garden cages: I would like to know how much sunlight the mesh lets through. I think I need to calculate the area of the mesh's negative space. And then ...
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find the area enclosed by $f(x)=x+\sin(x)$ and its inverse from $x=0$ to $x=2$ [closed]

I don't have a single clue to start, and we cant find the inverse so we must use some properties, but which ones? thanks
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How to calculate area of triangle-like structure of blocks? (Pick's Theorem seems insufficient.)

Given the following structure, is there a formula to calculate the number of blocks? (EDIT: and I am really looking for a solution for any BASE and HEIGHT.) At first, it would seem that this is a ...
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How do you find area of the loop in the graph of $x(x^2+y^2)=(x^2-y^2)$

The graph of the given equation is $x(x^2+y^2)=(x^2-y^2)$"> I believe I have to use (r,θ) coordinates but I do not know how to integrate this in (r,θ).
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Differential area for the lateral surface of frustum of a cone

I am studying Fluid Mechanics and I needed a differential area element of the side or lateral surface of a frustum. This frustum is cut from a cone. In solution manual of the book I study, ...
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Area defined by $x^2+y^2 \leq 1$ and $y\geq x(x^2-16)$

Area defined by $x^2+y^2 \leq 1$ and $y\geq x(x^2-16)$ One very obvious way would be to find the points of intersection which would be messy and subject to many conditions. I was trying to solve ...
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Find area using double integral and polar coordinates

Find the area enclosed by $ρ=1+cos(\theta)$. I can not find the angle of the function to define the limits of the integrals. This would be the graph of the function: What I was trying to do, because ...
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How can I find the volume generated by revolving the following region about $x=5$?

The region enclosed by : $y=6-x^2$ and $y=5$ I first get the inverse functions and the intersections and then work with the disk/washer method, the result is zero and I can't figure out what am I ...
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Calculate the area of the curve $\cfrac{e^x}{e^{2x}+9}$ between the x-axis

6.Calculate the area located on x-axis and below the curve $y=\cfrac{e^x}{e^{2x}+9}$ I've thinking of finding the intersection points of the curve and $y=0$ \begin{align} e^x& = 0 \qquad /\ln ...
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Triangle with two sides given find the greatest area if the area is prime number [closed]

A triangle has two sides of lengths 4 centimeters and 6 centimeters. Its area is n square centimeters, where n is a prime number. What is the greatest possible value of n? (A) 11 (B) 12 (C) 19 (D) 23 (...
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I have no idea how to solve this problem using areas of known cross section

The problem involving cross sections I am so confused on how to find volume using known cross sections. I've never understood it. This problem that I've encountered is very difficult, and I tried ...