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Assume the radius of a certain planet is 3840 km and the planet is a sphere. What is its surface area? The planet's surface area is (Type an exact answer, using ras needed.)

Ask by Johnston Gardner. in the United States
Feb 28,2025

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Answer

The planet's surface area is \( 58,982,400\pi \) square kilometers.

Solution

The formula for the surface area of a sphere is A = 4πr². Given r = 3840 km, substitute it into the formula:   A = 4π(3840)² First, calculate (3840)²:   3840² = 3840 × 3840 = 14,745,600 Now multiply by 4:   4 × 14,745,600 = 58,982,400 Thus, the planet’s surface area is:   58,982,400π km² That is the exact answer.

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Beyond the Answer

The formula for the surface area \(A\) of a sphere is given by the equation \(A = 4\pi r^2\), where \(r\) is the radius. For a planet with a radius of 3840 km, the calculations would look like this: \[ A = 4\pi (3840)^2 = 4\pi \times 14,745,600 \approx 185,105,843.866 \text{ km}^2. \] Thus, the planet's surface area is approximately \(185,105,843.87 \text{ km}^2\). And just for fun, if you were standing on this planet, you’d have a ton of space to explore—over 185 million square kilometers of cosmic adventure! That’s a whole lot of room for aliens to hide!

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