Mensuration – Surface Area and Volume✍ Written by: Sarthak Prakash Patil

 

<h2>Mensuration – Surface Area and Volume</h2>

<h3>1. Introduction</h3>

<p>Mensuration is the branch of mathematics that deals with the measurement of <b>length, area, and volume</b> of different shapes and solids.</p>

<h3>2. 2D Shapes and Formulas</h3>

<ol>

  <li><b>Square:</b><br>

    Area = a²<br>

    Perimeter = 4a

  </li>

  <li><b>Rectangle:</b><br>

    Area = l × b<br>

    Perimeter = 2(l+b)

  </li>

  <li><b>Triangle:</b><br>

    Area = ½ × base × height<br>

    Using Heron’s Formula:<br>

    √[s(s-a)(s-b)(s-c)], s = (a+b+c)/2

  </li>

  <li><b>Circle:</b><br>

    Area = πr²<br>

    Circumference = 2πr

  </li>

</ol>

<h3>3. 3D Solids and Formulas</h3>

<ol>

  <li><b>Cube:</b><br>

    Surface Area = 6a²<br>

    Volume = a³

  </li>

  <li><b>Cuboid:</b><br>

    Surface Area = 2(lb + bh + hl)<br>

    Volume = l × b × h

  </li>

  <li><b>Sphere:</b><br>

    Surface Area = 4πr²<br>

    Volume = (4/3)πr³

  </li>

  <li><b>Cylinder:</b><br>

    Curved Surface Area = 2πrh<br>

    Total Surface Area = 2πr(h+r)<br>

    Volume = πr²h

  </li>

</ol>

<h3>4. Application in Real Life</h3>

<ul>

  <li>Construction and architecture</li>

  <li>Designing containers and packaging</li>

  <li>Calculating land area and fencing length</li>

</ul>

<p><i>✍ Written by: Sarthak Prakash Patil</i></p>