## Task Condition

Calculate the volumes of bodies bounded by surfaces.

$$
z=2 x^{2}+18 y^{2}, z=6
$$
## Solution

$$
\begin{aligned}
& a=\frac{\sqrt{z}}{\sqrt{2}} ; b=\frac{\sqrt{z}}{\sqrt{18}} \\
& V=\frac{1}{6} \pi \int_{0}^{6} z d z=\left.\frac{1}{12} \pi z^{2}\right|_{0} ^{6}=3 \pi
\end{aligned}
$$

Source — "http://pluspi.org/wiki/index.php/?\?\?\?\?\?\?\?\?\?\?\? \%D0\%9A\%D1\%83\%D0\%B7\%D0\%BD\%D0\%B5\%D1\%86\%D0\%BE\%D0\%B2_\%D0\%98\%D0\%BD $\% \mathrm{D} 1 \% 82 \% \mathrm{D} 0 \% \mathrm{~B} \% \mathrm{D} 0 \% \mathrm{~B} 3 \% \mathrm{D} 1 \% 80 \% \mathrm{D} 0 \% \mathrm{~B} 0 \% \mathrm{D} 0 \% \mathrm{BB} \% \mathrm{D} 1 \% 8 \mathrm{~B}+20-27$ "

Categories: Kuznetsov Problem Book Integrals Problem 20 | Integrals

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## Problem Kuznetsov Integrals 20-28

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