Question
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
Upstudy AI Solution
Tutor-Verified Answer
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.
Answered by UpStudy AI and reviewed by a Professional Tutor
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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!