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Math·Geometry and Trigonometry·Area and volume

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For the right circular cone shown, $\overline{OP}$ is a radius of the base and $V$ is the vertex. The cone’s lateral surface area, in square meters, is $rL\pi$, where $L$ is the length, in meters, of $\overline{PV}$ and $r$ is the length, in meters, of $\overline{OP}$. The cone has a base area of $81\pi$ square meters and a lateral surface area of $128\pi$ square meters. What is the height of the cone, to the nearest meter?

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