A liquid covers approximately 70% of a planet's surface. Assume the planet is a sphere with a diameter of about 7400 km. What amount of the planet's surface is covered with the liquid?

a) [tex]2\pi \times 3700 \text{ km}^2[/tex]
b) [tex]\pi \times 3700 \text{ km}^2[/tex]
c) [tex]4\pi \times 3700 \text{ km}^2[/tex]
d) [tex]3\pi \times 3700 \text{ km}^2[/tex]

Question

25-05-2024
Geography

High School

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A liquid covers approximately 70% of a planet's surface. Assume the planet is a sphere with a diameter of about 7400 km. What amount of the planet's surface is covered with the liquid?

a) [tex]2\pi \times 3700 \text{ km}^2[/tex]
b) [tex]\pi \times 3700 \text{ km}^2[/tex]
c) [tex]4\pi \times 3700 \text{ km}^2[/tex]
d) [tex]3\pi \times 3700 \text{ km}^2[/tex]

Answer :

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abhisheksharma222023 abhisheksharma222023 · Answer 1 · 2024-02-11T07:44:04-05:00

Final answer:

The surface area of a planet covered with liquid is calculated using the sphere's surface area formula, 4πr², and then taking 70% of this value since 70% of the planet is covered with the liquid. The planet's radius is 3700 km, leading to an answer closest to 4π×3700 km².

Explanation:

The question asks to calculate the surface area of a planet covered with liquid, given that 70% of its surface is covered and the planet's diameter is 7400 km. To find the surface area, we use the formula for the area of a sphere, which is 4πr², where r is the radius of the sphere. Here, the radius is half of the diameter, i.e., 3700 km. Therefore, the total surface area of the planet is 4π(3700 km)². To get the surface area covered with liquid, we calculate 70% of the total surface area, which still uses the base form of the sphere's surface area formula. The correct answer, therefore, is closest to option c) 4π×3700 km², which represents the total surface area of the sphere (planet), but for the exact area covered with liquid, we would take 70% of this value.