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Area of cycloid given height Solution

STEP 0: Pre-Calculation Summary
Formula Used
area = 3*pi*(Height/2)^2
A = 3*pi*(h/2)^2
This formula uses 1 Constants, 1 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Height - Height is the distance between the lowest and highest points of a person standing upright. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Height: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = 3*pi*(h/2)^2 --> 3*pi*(12/2)^2
Evaluating ... ...
A = 339.292006587698
STEP 3: Convert Result to Output's Unit
339.292006587698 Square Meter --> No Conversion Required
FINAL ANSWER
339.292006587698 Square Meter <-- Area
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Volume of a Conical Frustum
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go
Total Surface Area of a Cone
total_surface_area = pi*Radius*(Radius+sqrt(Radius^2+Height^2)) Go
Lateral Surface Area of a Cone
lateral_surface_area = pi*Radius*sqrt(Radius^2+Height^2) Go
Total Surface Area of a Cylinder
total_surface_area = 2*pi*Radius*(Height+Radius) Go
Lateral Surface Area of a Cylinder
lateral_surface_area = 2*pi*Radius*Height Go
Volume of a Circular Cone
volume = (1/3)*pi*(Radius)^2*Height Go
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Volume of a Circular Cylinder
volume = pi*(Radius)^2*Height Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Area of a Triangle when base and height are given
area = 1/2*Base*Height Go
Area of a Parallelogram when base and height are given
area = Base*Height Go

11 Other formulas that calculate the same Output

Area of a Triangle when sides are given
area = sqrt((Side A+Side B+Side C)*(Side B+Side C-Side A)*(Side A-Side B+Side C)*(Side A+Side B-Side C))/4 Go
Area of a Rhombus when side and diagonals are given
area = (1/2)*(Diagonal A)*(sqrt(4*Side^2-(Diagonal A)^2)) Go
Area of a Rectangle when breadth and diagonal are given
area = Breadth*(sqrt((Diagonal)^2-(Breadth)^2)) Go
Area of a Rectangle when length and diagonal are given
area = Length*(sqrt((Diagonal)^2-(Length)^2)) Go
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Area of a Rhombus when diagonals are given
area = (Diagonal A*Diagonal B)/2 Go
Area of a Triangle when base and height are given
area = 1/2*Base*Height Go
Area of a Rectangle when length and breadth are given
area = Length*Breadth Go
Area of a Parallelogram when base and height are given
area = Base*Height Go
Area of a Square when diagonal is given
area = 1/2*(Diagonal)^2 Go
Area of a Square when side is given
area = (Side A)^2 Go

Area of cycloid given height Formula

area = 3*pi*(Height/2)^2
A = 3*pi*(h/2)^2

What is a cycloid?

In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity (the brachistochrone curve). It is also the form of a curve for which the period of an object in simple harmonic motion (rolling up and down repetitively) along the curve does not depend on the object's starting position (the tautochrone curve).

How to Calculate Area of cycloid given height?

Area of cycloid given height calculator uses area = 3*pi*(Height/2)^2 to calculate the Area, The Area of cycloid given height formula is defined as measure of the total area that the surface of the object occupies of a cycloid, where a = radius of cycloid, A = Area of cycloid. Area and is denoted by A symbol.

How to calculate Area of cycloid given height using this online calculator? To use this online calculator for Area of cycloid given height, enter Height (h) and hit the calculate button. Here is how the Area of cycloid given height calculation can be explained with given input values -> 339.292 = 3*pi*(12/2)^2.

FAQ

What is Area of cycloid given height?
The Area of cycloid given height formula is defined as measure of the total area that the surface of the object occupies of a cycloid, where a = radius of cycloid, A = Area of cycloid and is represented as A = 3*pi*(h/2)^2 or area = 3*pi*(Height/2)^2. Height is the distance between the lowest and highest points of a person standing upright.
How to calculate Area of cycloid given height?
The Area of cycloid given height formula is defined as measure of the total area that the surface of the object occupies of a cycloid, where a = radius of cycloid, A = Area of cycloid is calculated using area = 3*pi*(Height/2)^2. To calculate Area of cycloid given height, you need Height (h). With our tool, you need to enter the respective value for Height and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Area?
In this formula, Area uses Height. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • area = 1/2*Base*Height
  • area = sqrt((Side A+Side B+Side C)*(Side B+Side C-Side A)*(Side A-Side B+Side C)*(Side A+Side B-Side C))/4
  • area = Length*Breadth
  • area = Length*(sqrt((Diagonal)^2-(Length)^2))
  • area = Breadth*(sqrt((Diagonal)^2-(Breadth)^2))
  • area = (Side A)^2
  • area = 1/2*(Diagonal)^2
  • area = (Diagonal A*Diagonal B)/2
  • area = (1/2)*(Diagonal A)*(sqrt(4*Side^2-(Diagonal A)^2))
  • area = Base*Height
  • area = ((Base A+Base B)/2)*Height
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