Update index.html

Author: Gmac4247

index.html

@@ -186,7 +186,7 @@
 },
 "dateCreated" :"2019-01-11",
 "datePublished":"2020-01-11",
-"dateModified" :"2025-06-05",
+"dateModified" :"2025-06-26",
 "description" : "Introducing the best-established and most accurate framework to calculate area and volume.",
 "disambiguatingDescription": "Exact, empirically grounded and rigorously proven formulas over the conventional approximations.",
 "headline":"Exact geometry",
@@ -285,9 +285,9 @@
         "description": "The volume of a spherical cap based on the radius of the sphere and the cap.",
      "disambiguatingDescription": "More accurate than the conventional formula ",
 	"target": "https://basic-geometry.github.io/",
-     "mathExpression-input": "r1=5 r2=3 V=?",
-     "mathExpression-output": "1.6 * Math.pow(sphereSliceBottomRadius, 2) * Math.sqrt(3.2) * (1 - Math.sin(Math.acos(sphereSliceBottomRadius / sphereRadius)))", 
-     "image": "sphericalCap.jpg",
+     "mathExpression-input": "r=5 h=3 V=?",
+     "mathExpression-output": "1.6 * Math.pow(capRadius, 2) * Math.sqrt(3.2) * (1 - Math.cos(2 * Math.atan(capHeight / capRadius)))", 
+     "image": "sphericalCapMarkup.jpg",
      "eduQuestionType": "Volume calculation"
   },
 
@@ -1104,10 +1104,64 @@ <h6 style="font-size:160%;margin:7px">Area of a circle</h6>
 </h10>
 <br>
 <div class="imgbox">
-    <img class="center-fit" src="sphericalCap.jpg" alt="Sphere" id="cap">
+    <img class="center-fit" src="sphericalCapMarkup.jpg" alt="Sphere" id="cap">
     </div>
     <br>
-<p style="margin:12px;">Volume of a spherical cap:
+<p style="margin:12px;">In terms of cap radius and height:
+<br>
+<br>
+<math xmlns="http://www.w3.org/1998/Math/MathML" >
+<mrow>
+ <mi>V</mi>
+      <mo>=</mo>
+  <mn>1.6</mn>
+<mo>×</mo>
+ <msup>
+<mrow>
+<msub>
+<mi>r</mi>
+<mi>cap</mi>
+</msub>
+</mrow>
+<mn>2</mn>
+</msup>
+<mo>×</mo>
+<msqrt>
+<mn>3.2</mn>
+</msqrt>
+<mo>×</mo>
+<mo>(</mo>
+    <mn>1</mn>
+    <mo>-</mo>
+<mi>cos</mi>
+<mo>&#x2061;</mo>
+      <mrow>
+        <mo>(</mo>
+	      <mn>2</mn>
+    <mo>×</mo>
+          <mo>arctan</mo>
+    <mo>&#x2061;</mo>
+          <mo>(</mo>
+          <mfrac>
+            <mi>h</mi>
+<msub>
+<mi>r</mi>
+<mi>cap</mi>
+</msub>
+          </mfrac>
+          <mo>)</mo>
+        <mo>)</mo>
+       <mo>)</mo>
+      </mrow>
+  </mrow>
+</math>
+</p>
+</div>
+<br>
+<br>
+<br>
+<br>
+<p style="margin:12px;">In terms of radii:
 <br>
 <br>
 <math xmlns="http://www.w3.org/1998/Math/MathML" >