Circle Measurements Calculator for Radius and Area

Kihesabu cha Vipimo vya Mduara

Utangulizi

Mduara ni umbo la msingi katika jiometri, ukionyesha ukamilifu na usawa. Kihesabu chetu cha Vipimo vya Mduara kinakuwezesha kuhesabu radius, kipenyo, mzunguko, na eneo la mduara kulingana na kipimo kimoja kilichojulikana. Chombo hiki ni muhimu kwa wanafunzi, wahandisi, wasanifu, na mtu yeyote anayevutiwa na kuelewa mali za miduara.

Jinsi ya Kutumia Kihesabu Hiki

Chagua Kipimo Unachokijua:
- Radius
- Kipenyo
- Mzunguko
- Eneo
Ingiza Thamani:
- Ingiza thamani ya nambari kwa kipimo kilichochaguliwa.
- Hakikisha kwamba thamani ni nambari halisi chanya.
Hesabu:
- Kihesabu kitahesabu vipimo vingine vya mduara.
- Matokeo yanayoonyeshwa ni pamoja na:
  - Radius ( $r$ )
  - Kipenyo ( $d$ )
  - Mzunguko ( $C$ )
  - Eneo ( $A$ )

Uthibitishaji wa Ingizo

Kihesabu kinafanya ukaguzi ufuatao kwenye ingizo la mtumiaji:

Nambari Chanya: Ingizo zote lazima ziwe nambari halisi chanya.
Thamani za Nambari Halali: Ingizo lazima iwe za nambari na zisijumuisha wahusika wasio wa nambari.

Ikiwa ingizo zisizo sahihi zitagundulika, ujumbe wa kosa utaonyeshwa, na hesabu haitaanza hadi iporwe.

Mifumo

Mahusiano kati ya radius, kipenyo, mzunguko, na eneo la mduara yanafafanuliwa na mifumo ifuatayo:

Kipenyo ( $d$ ):

$d = 2r$
Mzunguko ( $C$ ):

$C = 2\pi r = \pi d$
Eneo ( $A$ ):

$A = \pi r^2 = \frac{\pi d^2}{4}$
Radius ( $r$ ) kutoka kwa Mzunguko:

$r = \frac{C}{2\pi}$
Radius ( $r$ ) kutoka kwa Eneo:

$r = \sqrt{\frac{A}{\pi}}$

Hesabu

Hapa kuna jinsi kihesabu kinavyohesabu kila kipimo kulingana na ingizo:

Wakati Radius ( $r$ ) Ijulikana:
- Kipenyo: $d = 2r$
- Mzunguko: $C = 2\pi r$
- Eneo: $A = \pi r^2$
Wakati Kipenyo ( $d$ ) Ijulikana:
- Radius: $r = \frac{d}{2}$
- Mzunguko: $C = \pi d$
- Eneo: $A = \frac{\pi d^2}{4}$
Wakati Mzunguko ( $C$ ) Ijulikana:
- Radius: $r = \frac{C}{2\pi}$
- Kipenyo: $d = \frac{C}{\pi}$
- Eneo: $A = \pi r^2$
Wakati Eneo ( $A$ ) Ijulikana:
- Radius: $r = \sqrt{\frac{A}{\pi}}$
- Kipenyo: $d = 2r$
- Mzunguko: $C = 2\pi r$

Mipaka na Usimamizi wa Ingizo

Ingizo Mbaya:
- Thamani mbaya si halali kwa vipimo vya mduara.
- Kihesabu kitaonyesha ujumbe wa kosa kwa ingizo mbaya.
Sifuri kama Ingizo:
- Sifuri ni ingizo halali lakini inasababisha vipimo vingine vyote kuwa sifuri.
- Kwa kimwili, mduara wenye vipimo sifuri haupo, hivyo kuingiza sifuri kunaweza kuwa kama kesi ya nadharia.
Thamani Kubwa Sana:
- Kihesabu kinaweza kushughulikia nambari kubwa sana, kulingana na usahihi wa lugha ya programu inayotumika.
- Kuwa makini na makosa ya kuzunguka kwa nambari kubwa sana.
Ingizo zisizo za nambari:
- Ingizo lazima iwe za nambari.
- Ingizo lolote lisilo la nambari litasababisha ujumbe wa kosa.

Matumizi

Kihesabu cha Vipimo vya Mduara ni muhimu katika matumizi mbalimbali ya ulimwengu halisi:

Uhandisi na Usanifu:
- Kubuni vipengele vya mduara kama vile mabomba, magurudumu, na arches.
- Kuamua mahitaji ya vifaa kwa miradi ya ujenzi inayohusisha umbo za mduara.
Utengenezaji:
- Kuamua vipimo vya sehemu na zana.
- Kuamua njia za kukata kwa mashine za CNC.
Astronomia na Sayansi ya Anga:
- Kuamua mizunguko ya sayari, ambayo mara nyingi inakisiwa kama miduara.
- Kadiria eneo la uso wa miili ya angani.
Maisha ya Kila Siku:
- Kupanga bustani za mduara, chemchemi, au meza za mduara.
- Kuamua kiasi cha uzio kinachohitajika kwa vizuizi vya mduara.

Mbadala

Ingawa miduara ni ya msingi, kuna umbo mbadala na mifumo kwa matumizi tofauti:

Mizunguko:
- Kwa matumizi yanayohitaji miduara iliyonyooka.
- Hesabu zinajumuisha ncha za mduara na ncha za mduara.
Sehemu na Sehemu za Mduara:
- Sehemu za mduara.
- Inatumika kwa kuhesabu maeneo au mipaka ya vipande vya keki.
Poligoni za Kawaida:
- Makaratasi ya miduara kwa kutumia umbo kama vile hexagoni au octagoni.
- Inarahisisha ujenzi na hesabu katika baadhi ya muktadha wa uhandisi.

Historia

Utafiti wa miduara unarudi nyuma kwa ustaarabu wa zamani:

Hisabati ya Kale:
- Wababiloni na Wamisri walitumia makadirio kwa $\pi$ .
- Archimedes (c. 287–212 BCE) alitoa moja ya algorithimu za kwanza zilizorekodiwa za kuhesabu $\pi$ , akikadiria kati ya $\frac{22}{7}$ na $\frac{223}{71}$ .
Maendeleo ya $\pi$ :
- Alama $\pi$ ilienezwa na mwanahisabati wa Uelsi William Jones mnamo 1706 na baadaye kupitishwa na Leonhard Euler.
- $\pi$ ni nambari isiyo na mwisho inayowakilisha uwiano wa mzunguko wa mduara kwa kipenyo chake.
Hisabati ya Kisasa:
- Mduara umekuwa katikati ya maendeleo katika trigonometry, calculus, na uchambuzi wa tata.
- Inatumika kama dhana ya msingi katika jiometri na uthibitisho wa kisayansi.

Mifano

Hapa chini kuna mifano ya msimbo inayoonyesha jinsi ya kuhesabu vipimo vya mduara katika lugha mbalimbali za programu:

1## Msimbo wa Python kuhesabu vipimo vya mduara
2import math
3
4def calculate_circle_from_radius(radius):
5    diameter = 2 * radius
6    circumference = 2 * math.pi * radius
7    area = math.pi * radius ** 2
8    return diameter, circumference, area
9
10## Matumizi ya mfano:
11radius = 5
12d, c, a = calculate_circle_from_radius(radius)
13print(f"Radius: {radius}")
14print(f"Kipenyo: {d}")
15print(f"Mzunguko: {c:.2f}")
16print(f"Eneo: {a:.2f}")
17

1// Msimbo wa JavaScript kuhesabu vipimo vya mduara
2function calculateCircleFromDiameter(diameter) {
3  const radius = diameter / 2;
4  const circumference = Math.PI * diameter;
5  const area = Math.PI * Math.pow(radius, 2);
6  return { radius, circumference, area };
7}
8
9// Matumizi ya mfano:
10const diameter = 10;
11const { radius, circumference, area } = calculateCircleFromDiameter(diameter);
12console.log(`Radius: ${radius}`);
13console.log(`Kipenyo: ${diameter}`);
14console.log(`Mzunguko: ${circumference.toFixed(2)}`);
15console.log(`Eneo: ${area.toFixed(2)}`);
16

1// Msimbo wa Java kuhesabu vipimo vya mduara
2public class CircleCalculator {
3    public static void calculateCircleFromCircumference(double circumference) {
4        double radius = circumference / (2 * Math.PI);
5        double diameter = 2 * radius;
6        double area = Math.PI * Math.pow(radius, 2);
7
8        System.out.printf("Radius: %.2f%n", radius);
9        System.out.printf("Kipenyo: %.2f%n", diameter);
10        System.out.printf("Mzunguko: %.2f%n", circumference);
11        System.out.printf("Eneo: %.2f%n", area);
12    }
13
14    public static void main(String[] args) {
15        double circumference = 31.42;
16        calculateCircleFromCircumference(circumference);
17    }
18}
19

1// Msimbo wa C# kuhesabu vipimo vya mduara
2using System;
3
4class CircleCalculator
5{
6    static void CalculateCircleFromArea(double area)
7    {
8        double radius = Math.Sqrt(area / Math.PI);
9        double diameter = 2 * radius;
10        double circumference = 2 * Math.PI * radius;
11
12        Console.WriteLine($"Radius: {radius:F2}");
13        Console.WriteLine($"Kipenyo: {diameter:F2}");
14        Console.WriteLine($"Mzunguko: {circumference:F2}");
15        Console.WriteLine($"Eneo: {area:F2}");
16    }
17
18    static void Main()
19    {
20        double area = 78.54;
21        CalculateCircleFromArea(area);
22    }
23}
24

1## Msimbo wa Ruby kuhesabu vipimo vya mduara
2def calculate_circle_from_radius(radius)
3  diameter = 2 * radius
4  circumference = 2 * Math::PI * radius
5  area = Math::PI * radius ** 2
6  return diameter, circumference, area
7end
8
9## Matumizi ya mfano:
10radius = 5.0
11diameter, circumference, area = calculate_circle_from_radius(radius)
12puts "Radius: #{radius}"
13puts "Kipenyo: #{diameter}"
14puts "Mzunguko: #{circumference.round(2)}"
15puts "Eneo: #{area.round(2)}"
16

1<?php
2// Msimbo wa PHP kuhesabu vipimo vya mduara
3function calculateCircleFromDiameter($diameter) {
4    $radius = $diameter / 2;
5    $circumference = pi() * $diameter;
6    $area = pi() * pow($radius, 2);
7    return array($radius, $circumference, $area);
8}
9
10// Matumizi ya mfano:
11$diameter = 10.0;
12list($radius, $circumference, $area) = calculateCircleFromDiameter($diameter);
13echo "Radius: " . $radius . "\n";
14echo "Kipenyo: " . $diameter . "\n";
15echo "Mzunguko: " . round($circumference, 2) . "\n";
16echo "Eneo: " . round($area, 2) . "\n";
17?>
18

1// Msimbo wa Rust kuhesabu vipimo vya mduara
2fn calculate_circle_from_circumference(circumference: f64) -> (f64, f64, f64) {
3    let radius = circumference / (2.0 * std::f64::consts::PI);
4    let diameter = 2.0 * radius;
5    let area = std::f64::consts::PI * radius.powi(2);
6    (radius, diameter, area)
7}
8
9fn main() {
10    let circumference = 31.42;
11    let (radius, diameter, area) = calculate_circle_from_circumference(circumference);
12    println!("Radius: {:.2}", radius);
13    println!("Kipenyo: {:.2}", diameter);
14    println!("Mzunguko: {:.2}", circumference);
15    println!("Eneo: {:.2}", area);
16}
17

1// Msimbo wa Go kuhesabu vipimo vya mduara
2package main
3
4import (
5    "fmt"
6    "math"
7)
8
9func calculateCircleFromArea(area float64) (radius, diameter, circumference float64) {
10    radius = math.Sqrt(area / math.Pi)
11    diameter = 2 * radius
12    circumference = 2 * math.Pi * radius
13    return
14}
15
16func main() {
17    area := 78.54
18    radius, diameter, circumference := calculateCircleFromArea(area)
19    fmt.Printf("Radius: %.2f\n", radius)
20    fmt.Printf("Kipenyo: %.2f\n", diameter)
21    fmt.Printf("Mzunguko: %.2f\n", circumference)
22    fmt.Printf("Eneo: %.2f\n", area)
23}
24

1// Msimbo wa Swift kuhesabu vipimo vya mduara
2import Foundation
3
4func calculateCircleFromRadius(radius: Double) -> (diameter: Double, circumference: Double, area: Double) {
5    let diameter = 2 * radius
6    let circumference = 2 * Double.pi * radius
7    let area = Double.pi * pow(radius, 2)
8    return (diameter, circumference, area)
9}
10
11// Matumizi ya mfano:
12let radius = 5.0
13let results = calculateCircleFromRadius(radius: radius)
14print("Radius: \(radius)")
15print("Kipenyo: \(results.diameter)")
16print("Mzunguko: \(String(format: "%.2f", results.circumference))")
17print("Eneo: \(String(format: "%.2f", results.area))")
18

1% Msimbo wa MATLAB kuhesabu vipimo vya mduara
2function [radius, diameter, circumference, area] = calculateCircleFromRadius(radius)
3    diameter = 2 * radius;
4    circumference = 2 * pi * radius;
5    area = pi * radius^2;
6end
7
8% Matumizi ya mfano:
9radius = 5;
10[~, diameter, circumference, area] = calculateCircleFromRadius(radius);
11fprintf('Radius: %.2f\n', radius);
12fprintf('Kipenyo: %.2f\n', diameter);
13fprintf('Mzunguko: %.2f\n', circumference);
14fprintf('Eneo: %.2f\n', area);
15

1' Msimbo wa Excel kuhesabu vipimo vya mduara kutoka radius
2' Ikiwa radius iko kwenye seli A1
3Kipenyo: =2*A1
4Mzunguko: =2*PI()*A1
5Eneo: =PI()*A1^2
6

Mifano ya Nambari

Iliyopewa Radius (( r = 5 ) vitengo):
- Kipenyo: ( d = 2 \times 5 = 10 ) vitengo
- Mzunguko: ( C = 2\pi \times 5 \approx 31.42 ) vitengo
- Eneo: ( A = \pi \times 5^2 \approx 78.54 ) vitengo vya mraba
Iliyopewa Kipenyo (( d = 10 ) vitengo):
- Radius: ( r = \frac{10}{2} = 5 ) vitengo
- Mzunguko: ( C = \pi \times 10 \approx 31.42 ) vitengo
- Eneo: ( A = \frac{\pi \times 10^2}{4} \approx 78.54 ) vitengo vya mraba
Iliyopewa Mzunguko (( C = 31.42 ) vitengo):
- Radius: ( r = \frac{31.42}{2\pi} \approx 5 ) vitengo
- Kipenyo: ( d = 2 \times 5 = 10 ) vitengo
- Eneo: ( A = \pi \times 5^2 \approx 78.54 ) vitengo vya mraba
Iliyopewa Eneo (( A = 78.54 ) vitengo vya mraba):
- Radius: ( r = \sqrt{\frac{78.54}{\pi}} \approx 5 ) vitengo
- Kipenyo: ( d = 2 \times 5 = 10 ) vitengo
- Mzunguko: ( C = 2\pi \times 5 \approx 31.42 ) vitengo

Mchoro

Hapa chini kuna mchoro wa mduara unaoonyesha radius (( r )), kipenyo (( d )), mzunguko (( C )), na eneo (( A )).

Picha: Mchoro wa mduara unaoonyesha radius (( r )), kipenyo (( d )), mzunguko (( C )), na eneo (( A )).

Marejeleo

"Mduara." Wolfram MathWorld, https://mathworld.wolfram.com/Circle.html.
"Mzunguko na Eneo la Mduara." Khan Academy, https://www.khanacademy.org/math/basic-geo/basic-geo-circles.
Beckmann, Petr. Historia ya ( \pi ). St. Martin's Press, 1971.
Archimedes. Kipimo cha Mduara, https://www.math.ubc.ca/~vjungic/students/Archimedes-Measurement%20of%20a%20Circle.pdf.

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