Question

Related Rates conical tank more info in comments

Answer 1

I'm confused by this answer key. At the very bottom of the second column it states
v = 1/3 pie (3h/4)^2 h. Doesn't that mean 9h^3/48 pie ?

Answer 2

<math xmlns=" http://www.w3.org/1998/Math/MathML ">
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mstyle mathsize="2.49em">
<mstyle mathcolor="gold">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
</mstyle>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle mathsize="2.49em">
<mrow class="MJX-TeXAtom-ORD">
<mpadded width="0">
<mspace width="2em" />
<mspace width="2em" />
<mrow class="MJX-TeXAtom-ORD">
<mspace width="thickmathspace" />
<mspace width="thinmathspace" />
<mi mathvariant="bold">w</mi>
<mi mathvariant="bold">e</mi>
<mi mathvariant="bold">c</mi>
<mi mathvariant="bold">o</mi>
<mi mathvariant="bold">m</mi>
<mi mathvariant="bold">e</mi>
<mtext>&#xA0;</mtext>
<mi mathvariant="bold">t</mi>
<mi mathvariant="bold">o</mi>
</mrow>
</mpadded>
</mrow>
<mstyle mathbackground="gold" style="border:2px solid red">
<mpadded width="+10pt" height="+5pt" depth="+5pt" lspace="5pt">
<mspace width="2em" />
<mspace width="2em" />
<mstyle mathcolor="red">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">w</mi>
<mi mathvariant="bold">e</mi>
<mi mathvariant="bold">c</mi>
<mi mathvariant="bold">o</mi>
<mi mathvariant="bold">m</mi>
<mi mathvariant="bold">e</mi>
<mtext>&#xA0;</mtext>
<mi mathvariant="bold">t</mi>
<mi mathvariant="bold">o</mi>
</mrow>
</mstyle>
<mspace width="2em" />
<mspace width="2em" />
<mspace width="1em" />
</mpadded>
</mstyle>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle mathsize="2.49em">
<mrow class="MJX-TeXAtom-ORD">
<mpadded width="0">
<mrow class="MJX-TeXAtom-ORD">
<mspace width="thinmathspace" />
<mspace width="thickmathspace" />
<mi mathvariant="bold">o</mi>
<mi mathvariant="bold">p</mi>
<mi mathvariant="bold">e</mi>
<mi mathvariant="bold">n</mi>
<mtext>&#xA0;</mtext>
<mi mathvariant="bold">s</mi>
<mi mathvariant="bold">t</mi>
<mi mathvariant="bold">u</mi>
<mi mathvariant="bold">d</mi>
<mi mathvariant="bold">y</mi>
<mo mathvariant="bold">!</mo>
</mrow>
</mpadded>
</mrow>
<mstyle mathbackground="gold" style="border:2px solid red">
<mpadded width="+10pt" height="+5pt" depth="+5pt" lspace="5pt">
<mstyle mathcolor="red">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">o</mi>
<mi mathvariant="bold">p</mi>
<mi mathvariant="bold">e</mi>
<mi mathvariant="bold">n</mi>
<mtext>&#xA0;</mtext>
<mi mathvariant="bold">s</mi>
<mi mathvariant="bold">t</mi>
<mi mathvariant="bold">u</mi>
<mi mathvariant="bold">d</mi>
<mi mathvariant="bold">y</mi>
<mo mathvariant="bold">!</mo>
</mrow>
</mstyle>
</mpadded>
</mstyle>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle mathsize="2.49em">
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mstyle mathcolor="gold">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle mathcolor="gold">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle mathcolor="gold">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
</mstyle>
</mtd>
</mtr>
</mtable>
<mstyle mathcolor="purple">
<mover>
<mrow>
<mo>(</mo>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mstyle mathcolor="blue">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mo>&#x2299;<!-- ⊙ --></mo>
<mo>&#x005E;<!-- ^ --></mo>
</mover>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mo>&#x2299;<!-- ⊙ --></mo>
<mo>&#x005E;<!-- ^ --></mo>
</mover>
</mrow>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle mathsize="0.85em">
<mo>&#x25B3;<!-- △ --></mo>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle>
<mstyle mathcolor="red">
<mo>&#x2323;<!-- ⌣ --></mo>
</mstyle>
</mstyle>
</mtd>
</mtr>
</mtable>
<mo>)</mo>
</mrow>
<mo accent="false">&#x23DE;<!-- ⏞ --></mo>
</mover>
</mstyle>
<mstyle>
<mtable rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mstyle mathcolor="gold">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle mathcolor="gold">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
</mstyle>
</mtd>
</mtr>
<mtr>
<mtd>
<mstyle mathcolor="gold">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2605;</mo>
</mrow>
</mstyle>
</mtd>
</mtr>
</mtable>
</mstyle>
</mstyle>
</mtd>
</mtr>
</mtable>