{"id":9747,"date":"2025-09-23T20:22:07","date_gmt":"2025-09-23T14:52:07","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=9747"},"modified":"2025-09-23T22:18:45","modified_gmt":"2025-09-23T16:48:45","slug":"area-of-quadrant-of-a-circle","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/area-of-quadrant-of-a-circle\/","title":{"rendered":"Area of quadrant of a circle"},"content":{"rendered":"\n

TL;DR<\/mark><\/strong>
The area of a quadrant equals one-quarter of the circle’s total area and uses the formula: Area = ?r\u00b2\/4, with r representing the circle’s radius. Since each quadrant covers exactly 25% of the complete circle, this calculation divides the full circle area by four. For instance, when a circle has an 8 cm radius, the quadrant area becomes (? \u00d7 8\u00b2)\/4 = 16? cm\u00b2.<\/strong><\/p>\n\n\n\n

Quadrant of a Circle<\/h2>\n\n\n\n

A quadrant<\/strong> is one of four equal parts of a circle. Imagine drawing two lines across the circle: one horizontal and one vertical, both passing right through the centre, and making a perfect right angle (90 degrees) between them. These lines divide the circle into four equal sections called quadrants.<\/p>\n\n\n\n

\n

Each quadrant represents one-fourth of the entire circle. So, the area of a quadrant is one-fourth the area of the whole circle.<\/p>\n<\/blockquote>\n\n\n\n

\n\n\n\n
\"Quarter<\/a><\/figure>\n\n\n\n

All four quadrants have identical areas and shapes, making each one exactly 25% of the complete circle.<\/p>\n\n\n\n

Area of a Circle Recap<\/h2>\n\n\n\n

Before finding the area of a quadrant, we should know how to find the area of the full circle. The formula for the area of a circle is:
$$
\\text{Area of Circle} = \\pi \\times r^2
$$<\/p>\n\n\n\n

Here, $r$ is the radius \u2014 the distance from the centre of the circle to any point on its edge. The symbol $\\pi$ (pi) is a constant approximately equal to 3.1416.<\/p>\n\n\n\n

\"Area<\/a><\/figure>\n\n\n\n
\n\n\n\n

Finding the Area of a Quadrant<\/h2>\n\n\n\n

Since a quadrant is exactly one-fourth of the circle, its area is:
$$
\\text{Area of Quadrant} = \\frac{1}{4} \\times \\pi r^2
$$
This means to find the area of a quadrant, we calculate the whole circle\u2019s area first, and then divide it by 4.<\/p>\n\n\n\n

\"Area<\/a><\/figure>\n\n\n\n

Step-by-step process:<\/h2>\n\n\n\n
    \n
  1. Find or measure the radius $r$.<\/li>\n\n\n\n
  2. Calculate the area of the whole circle using the formula $\\pi r^2$.<\/li>\n\n\n\n
  3. Divide that area by 4 to get the area of the quadrant.<\/li>\n\n\n\n
  4. Write the answer with square units (such as cm\u00b2, m\u00b2, inch\u00b2).<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Example 1: Area of a Quadrant with Radius 6 cm<\/h2>\n\n\n\n

    If the radius of the circle is 6 cm:<\/p>\n\n\n\n

      \n
    • The area of the circle is $\\pi \\times 6^2 = \\pi \\times 36 = 36\\pi \\text{ cm}^2$.<\/li>\n\n\n\n
    • Area of the quadrant = $\\frac{1}{4} \\times 36\\pi = 9\\pi \\text{ cm}^2$.<\/li>\n<\/ul>\n\n\n\n

      Approximating $\\pi$ as 3.14, the area equals about $9 \\times 3.14 = 28.26 \\text{ cm}^2$.<\/p>\n\n\n\n

      \n\n\n\n

      Example 2: Finding Radius from Quadrant Area<\/h2>\n\n\n\n

      Suppose the area of a quadrant is $16\\pi \\text{ cm}^2$. To find the radius:<\/p>\n\n\n\n

        \n
      • Use $\\frac{1}{4} \\pi r^2 = 16 \\pi$.<\/li>\n\n\n\n
      • Divide both sides by $\\pi$: $\\frac{1}{4} r^2 = 16$.<\/li>\n\n\n\n
      • Multiply both sides by 4: $r^2 = 64$.<\/li>\n\n\n\n
      • Take the square root: $r = 8 \\text{ cm}$.<\/li>\n<\/ul>\n\n\n\n

        So, the radius is 8 cm.<\/p>\n\n\n\n

        \n\n\n\n

        Additional Notes on Diameter and Circumference<\/h2>\n\n\n\n

        The diameter $d$ is twice the radius: $d = 2r$. The formula for the area of a quadrant can be rewritten in terms of diameter:
        $$
        \\text{Area of Quadrant} = \\frac{1}{16} \\pi d^2
        $$
        If given circumference $C = 2 \\pi r$, solve for radius:
        $$
        r = \\frac{C}{2\\pi}
        $$
        and then use this radius in the quadrant area formula.<\/p>\n\n\n\n

        \n\n\n\n

        Area of quadrant of a circle calculator<\/h2>\n\n\n\n
        \n \n

        \n Area of Circle Quadrant Calculator\n <\/h3>\n \n \n
        \n Formula:<\/strong> Area = \u00bc \u00d7 π \u00d7 r\u00b2<\/span>\n
        Where r is the radius of the circle<\/small>\n <\/div>\n \n \n
        \n