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Omni-MATH / On a spherical planet with diameter 10,000 mathrm{~km}, powerful explosives are placed at the north and south poles. The explosives are designed to vaporize all matter within …

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problem

On a spherical planet with diameter $10,000 \mathrm{~km}$, powerful explosives are placed at the north and south poles. The explosives are designed to vaporize all matter within $5,000 \mathrm{~km}$ of ground zero and leave anything beyond $5,000 \mathrm{~km}$ untouched. After the explosives are set off, what is the new surface area of the planet, in square kilometers?
Plain-text mathematical notation (without MathML)
On a spherical planet with diameter $10,000 \mathrm{~km}$, powerful explosives are placed at the north and south poles. The explosives are designed to vaporize all matter within $5,000 \mathrm{~km}$ of ground zero and leave anything beyond $5,000 \mathrm{~km}$ untouched. After the explosives are set off, what is the new surface area of the planet, in square kilometers?
Original LaTeX notation
On a spherical planet with diameter $10,000 \mathrm{~km}$, powerful explosives are placed at the north and south poles. The explosives are designed to vaporize all matter within $5,000 \mathrm{~km}$ of ground zero and leave anything beyond $5,000 \mathrm{~km}$ untouched. After the explosives are set off, what is the new surface area of the planet, in square kilometers?

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