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<p>The diagram shows a solid object made by cutting away a small cone from the big cone. <br></p>
<p>The base radii of the small and big cones are $3$ cm and $9$ cm respectively. The slant heights of the small and big cone are $6$ cm and $18$ cm respectively. Calculate the volume of the solid object.<br></p>
<div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765198005035-j5mebk9gch9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTgwMDUwMzUtajVtZWJrOWdjaDkucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDY5NSwiZXhwIjoxNzkyODUwOTk1fQ.jS1s_9IUFnvzk9Vx4NHkfkBb7RZP7XANeCgJBoknDLg" style="max-width: min(210px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div>

The diagram shows a solid object made by cutting away a small cone from the big cone. 


The base radii of the small and big cones are $3$ cm and $9$ cm respectively. The slant heights of the small and big cone are $6$ cm and $18$ cm respectively. Calculate the volume of the solid object.


Volume and Surface Area of Conical Frustums

Frustum-Type Solid: Volume Calculation

Mensuration (Pyramid, Cones and Spheres)

<p>The upper part of a solid wooden right circular cone is cut off leaving the frustum shown in the diagram. The height of the original cone, $VO$ is $18$ cm and the base radius, $OA$ is $9$ cm. The radius, $BC$, of the upper part is $6$ cm. Take $\pi $ to be $3.142$.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">Name the two similar triangles in the figure below.</div></li><li><div class="list-item-paragraph">Hence, show that&nbsp;$VC=12$ cm.</div></li><li><div class="list-item-paragraph">Hence, calculate the volume of the frustum, correct to $3$ significant figures.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1769848831649-lfqmqi0y6uf.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njk4NDg4MzE2NDktbGZxbXFpMHk2dWYucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDY5NSwiZXhwIjoxNzkyODUwOTk1fQ.S0jL1qHQ4b9mzEeQJUnleEn_Xrq0o_ZtaqP1FK7svHs" style="max-width: min(250px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The upper part of a solid wooden right circular cone is cut off leaving the frustum shown in the diagram. The height of the original cone, $VO$ is $18$ cm and the base radius, $OA$ is $9$ cm. The radius, $BC$, of the upper part is $6$ cm. Take $\pi $ to be $3.142$.

Volume of a Frustum and Similar Triangles

<p>The figure above shows two solid cones $VCB$ and $VOA$.<br>$BC=6$cm, $OA=9$cm and the vertical height of the cone $VOA$ is $12$ cm.<br>A frustum $OABC$ is obtained by removing the smaller cone $VCB$ from the larger cone $VOA$, find</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">$VC$,</div></li><li><div class="list-item-paragraph">the volume of frustum $OABC$.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1765195963099-j87eztw9dit.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NjUxOTU5NjMwOTktajg3ZXp0dzlkaXQucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5Mjg1MDY5NSwiZXhwIjoxNzkyODUwOTk1fQ.OGNOWYEWK9OtcXnrZrh_ShgkOvYxLG4AyaXdVFonL8E" style="max-width: min(230px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

The figure above shows two solid cones $VCB$ and $VOA$.
$BC=6$cm, $OA=9$cm and the vertical height of the cone $VOA$ is $12$ cm.
A frustum $OABC$ is obtained by removing the smaller cone $VCB$ from the larger cone $VOA$, find

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