@@ -2418,15 +2418,17 @@ <h3 itemprop="name" style="margin:7px">Calculate the Area of a Circle</h3>
24182418</ section >
24192419< div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToSection ">
24202420< meta itemprop ="position " content ="2 ">
2421- < div style =" margin:12px " itemprop ="itemListElement " itemscope itemtype ="https://schema.org/HowToStep ">
2421+ < div itemprop ="itemListElement " itemscope itemtype ="https://schema.org/HowToStep ">
24222422< meta itemprop ="position " content ="1 ">
24232423< p itemprop ="abstract "> The area of both the square and the sum of the quadrants equals 16 right triangles with legs of a quarter, and a half of the square's sides, and its hypotenuse equal to the radius of the circle.</ p >
24242424< br >
24252425< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
2426+ < meta itemprop ="description " content ="Exact circle area formula ">
24262427< span itemprop ="name "> A< sub > (circle)</ sub > </ span > =
24272428< span itemprop ="value ">
24282429< math xmlns ="http://www.w3.org/1998/Math/MathML ">
24292430< mrow >
2431+ < mrow >
24302432< mfrac >
24312433< mn > 16</ mn >
24322434< mn > 5</ mn >
@@ -2437,17 +2439,7 @@ <h3 itemprop="name" style="margin:7px">Calculate the Area of a Circle</h3>
24372439< mn > 2</ mn >
24382440</ msup >
24392441</ mrow >
2440- </ math >
2441- </ span >
2442- </ div >
2443- </ div >
2444- < br >
2445- < div style ="margin:12px " itemprop ="itemListElement " itemscope itemtype ="https://schema.org/HowToStep ">
2446- < meta itemprop ="position " content ="2 ">
2447- < div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
2448- < span itemprop ="name "> A< sub > (circle)</ sub > </ span > =
2449- < span itemprop ="value ">
2450- < math xmlns ="http://www.w3.org/1998/Math/MathML ">
2442+ < mo > =</ mo >
24512443< mrow >
24522444< mn > 3.2</ mn >
24532445< mo > ⁢</ mo > <!-- invisible times -->
@@ -2456,6 +2448,7 @@ <h3 itemprop="name" style="margin:7px">Calculate the Area of a Circle</h3>
24562448< mn > 2</ mn >
24572449</ msup >
24582450</ mrow >
2451+ </ mrow >
24592452</ math >
24602453</ span >
24612454</ div >
@@ -2985,12 +2978,13 @@ <h4>The true Ratio: 3.2</h4>
29852978</ div >
29862979</ details >
29872980< br >
2988- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
2981+ < div style =" margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
29892982< meta itemprop ="position " content ="8 ">
2990- < p itemprop ="description " style =" margin:12px " > The length of the circumference approaches 6.4 × radius as its thickness approaches 0.</ p >
2983+ < p itemprop ="description "> The length of the circumference approaches 6.4 × radius as its thickness approaches 0.</ p >
29912984< br >
29922985< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
2993- < span itemprop ="name "> Circumference</ span > =
2986+ < meta itemprop ="description " content ="Exact circumference formula ">
2987+ < span itemprop ="name "> Circumference</ span > =
29942988< span itemprop ="value ">
29952989< math xmlns ="http://www.w3.org/1998/Math/MathML ">
29962990< mrow >
@@ -3211,9 +3205,10 @@ <h3 itemprop="name" style="margin:7px">Calculate the Area of a Circle Segment</h
32113205< p itemprop ="abstract "> The height of the triangle is the segment height subtracted from the radius of the parent circle.</ p >
32123206</ details >
32133207< br >
3214- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
3208+ < div style =" margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
32153209< meta itemprop ="position " content ="4 ">
32163210< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
3211+ < meta itemprop ="description " content ="Exact circle segment area formula ">
32173212< span itemprop ="name "> A< sub > (segment)</ sub > </ span > =
32183213< span itemprop ="value ">
32193214< math xmlns ="http://www.w3.org/1998/Math/MathML ">
@@ -3607,8 +3602,9 @@ <h3 itemprop="name" style="margin:7px">Calculate the Surface Area of a Cone</h3>
36073602</ div >
36083603</ details >
36093604< br >
3610- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
3605+ < div style =" margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
36113606< meta itemprop ="position " content ="8 ">
3607+ < meta itemprop ="description " content ="Exact cone surface area formula ">
36123608< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
36133609< span itemprop ="name "> Surface< sub > (cone)</ sub > </ span > =
36143610< span itemprop ="value ">
@@ -3794,8 +3790,9 @@ <h3 itemprop="name" style="margin:7px">Calculate the Volume of a Sphere</h3>
37943790< br >
37953791</ details >
37963792< br >
3797- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
3798- < meta itemprop ="position " content ="7 ">
3793+ < div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
3794+ < meta itemprop ="position " content ="3 ">
3795+ < meta itemprop ="description " content ="Exact sphere volume formula ">
37993796< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
38003797< span itemprop ="name "> V< sub > (sphere)</ sub > </ span > =
38013798< span itemprop ="value ">
@@ -3909,8 +3906,9 @@ <h3 itemprop="name" style="margin:7px">Calculate the Volume of a Spherical Cap</
39093906< p style ="margin:12px " itemprop ="description "> One dimension of the volume of sphere formula can be adjusted to calculate the volume of a spherical cap as a distorted hemisphere.</ p >
39103907</ div >
39113908< br >
3912- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
3909+ < div style =" margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
39133910< meta itemprop ="position " content ="2 ">
3911+ < meta itemprop ="description " content ="Spherical cap volume formula ">
39143912< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
39153913< span itemprop ="name "> V< sub > (cap)</ sub > </ span > =
39163914< span itemprop ="value ">
@@ -4215,7 +4213,7 @@ <h4 itemprop="description">The volume of a cone can be calculated by algebraical
42154213</ figure >
42164214< br >
42174215< div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4218- < meta itemprop ="position " content ="3 ">
4216+ < meta itemprop ="position " content ="2 ">
42194217< p itemprop ="abstract "> The base of the two shapes is a quadrant circle.</ p >
42204218< br >
42214219< math xmlns ="http://www.w3.org/1998/Math/MathML " >
@@ -4271,7 +4269,7 @@ <h4 itemprop="description">The volume of a cone can be calculated by algebraical
42714269</ div >
42724270< br > < br >
42734271< div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4274- < meta itemprop ="position " content ="4 ">
4272+ < meta itemprop ="position " content ="3 ">
42754273< p itemprop ="abstract "> The slant height of the quadrant cone is √2 × radius.</ p >
42764274</ div >
42774275< br >
@@ -4308,7 +4306,7 @@ <h4 itemprop="description">The volume of a cone can be calculated by algebraical
43084306</ div >
43094307< br > < br >
43104308< div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4311- < meta itemprop ="position " content ="6 ">
4309+ < meta itemprop ="position " content ="4 ">
43124310< p itemprop ="abstract "> The slant form has a triangular vertical cross-section.
43134311< br >
43144312The area of a cone's vertical middle cross-section is the half of a cylinder with equal base and height.
@@ -4354,8 +4352,9 @@ <h4 itemprop="description">The volume of a cone can be calculated by algebraical
43544352</ div >
43554353</ div >
43564354< br >
4357- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4358- < meta itemprop ="position " content ="7 ">
4355+ < div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4356+ < meta itemprop ="position " content ="5 ">
4357+ < meta itemprop ="description " content ="Exact cone volume formula ">
43594358< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
43604359< span itemprop ="name "> V< sub > (cone)</ sub > </ span > =
43614360< span itemprop ="value ">
@@ -4606,8 +4605,9 @@ <h4 itemprop="abstract">The height of the theoretical full cone can be calculate
46064605</ math >
46074606</ div >
46084607< br >
4609- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4610- < meta itemprop ="position " content ="7 ">
4608+ < div style ="margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4609+ < meta itemprop ="position " content ="6 ">
4610+ < meta itemprop ="description " content ="Exact frustum cone volume formula ">
46114611< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
46124612< span itemprop ="name "> V< sub > (frustum)</ sub > </ span > =
46134613< span itemprop ="value ">
@@ -4843,8 +4843,9 @@ <h4 itemprop="description" style="margin:12px">The volume of a pyramid can be ca
48434843 < img class ="center-fit " src ="tetraFrame.jpeg " alt ="The volume of a pyramid can be calculated with the same coefficient as the volume of a cone. Volume = base × height / √8 ">
48444844 </ figure >
48454845< br > < br >
4846- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4846+ < div style =" margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
48474847< meta itemprop ="position " content ="2 ">
4848+ < meta itemprop ="description " content ="Exact pyramid volume formula ">
48484849< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
48494850< span itemprop ="name "> V< sub > (pyramid)</ sub > </ span > =
48504851< span itemprop ="value ">
@@ -4948,8 +4949,9 @@ <h3 itemprop="name" style="margin:12px">Calculate the Volume of a Frustum Pyrami
49484949< p itemprop ="description "> The volume of a frustum pyramid can be calculated with the same method as the < a href ="#frustum_cone "> volume of a frustum cone</ a > </ p >
49494950</ div >
49504951< br >
4951- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
4952+ < div style =" margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
49524953< meta itemprop ="position " content ="2 ">
4954+ < meta itemprop ="description " content ="Exact frustum pyramid volume formula ">
49534955< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
49544956< span itemprop ="name "> V< sub > (frustum)</ sub > </ span > =
49554957< span itemprop ="value ">
@@ -5103,7 +5105,7 @@ <h3 itemprop="name" style="margin:12px">Calculate the Volume of a Frustum Pyrami
51035105< section itemscope itemtype ="https://schema.org/LearningResource " id ="square_frustum ">
51045106< h3 style ="margin:12px "> Calculate the Volume of a square Frustum</ h3 >
51055107< meta itemprop ="name " content ="Horizontal square frustum pyramid volume calculation ">
5106- < meta itemprop ="disambiguatingDescription " content ="Based on the exact volume of a pyramid - base × height / √8 -, instead of the base × height / 3 approximate. ">
5108+ < meta itemprop ="disambiguatingDescription " content ="Only for square frustum pyramids. Based on the exact volume of a pyramid - base × height / √8 -, instead of the base × height / 3 approximate. ">
51075109< br >
51085110< figure class ="imgbox ">
51095111 < img class ="center-fit " src ="squareFrustum.jpeg " alt ="Square frustum pyramid ">
@@ -5139,6 +5141,7 @@ <h3 style="margin:12px">Calculate the Volume of a square Frustum</h3>
51395141</ div >
51405142< br >
51415143< div style ="margin:12px " itemprop ="description ">
5144+ < meta itemprop ="description " content ="Exact square frustum pyramid volume formula ">
51425145< span > V< sub > (square frustum)</ sub > </ span > =
51435146< span >
51445147< math xmlns ="http://www.w3.org/1998/Math/MathML ">
@@ -5487,8 +5490,9 @@ <h3 itemprop="name" style="margin:7px">Calculate the Volume of a Tetrahedron</h3
54875490</ div >
54885491</ details >
54895492< br >
5490- < div itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
5493+ < div style =" margin:12px " itemprop ="step " itemscope itemtype ="https://schema.org/HowToStep ">
54915494< meta itemprop ="position " content ="7 ">
5495+ < meta itemprop ="description " content ="Exact tetrahedron volume formula ">
54925496< div itemprop ="about " itemscope itemtype ="https://schema.org/PropertyValue ">
54935497< span itemprop ="name "> V< sub > (tetrahedron)</ sub > </ span > =
54945498< span itemprop ="value ">
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