{"status": "success", "data": {"description_md": "**POTD April 22, 2024**\n\nA spherical, three-dimensional planet has center at $(0,0, 0)$ and radius $20.$ At any point $(x,y,z)$ on the\nsurface of this planet, the temperature is $T(x,y, z) :=(x + y)^2 + (y - z)^2$ degrees. If the average temperature of the surface of this planet can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, find the value of $m+n$.", "description_html": "<p><strong>POTD April 22, 2024</strong></p>&#10;<p>A spherical, three-dimensional planet has center at <span class=\"katex--inline\">(0,0, 0)</span> and radius <span class=\"katex--inline\">20.</span> At any point <span class=\"katex--inline\">(x,y,z)</span> on the<br/>&#10;surface of this planet, the temperature is <span class=\"katex--inline\">T(x,y, z) :=(x + y)^2 + (y - z)^2</span> degrees. If the average temperature of the surface of this planet can be expressed as <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers, find the value of <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #134", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}