Math Problem Statement

Earth is approximately a sphere with a radius of 6400 km.

a  Calculate the surface area of Earth, correct to the nearest 10 square kilometres.

b  Approximately 70% of Earth’s surface is water. What area of Earth’s surface is covered with water?

c  What area of Earth’s surface is land?

Solution

Let's break down the problem and solve it step by step.

Part (a): Calculate the surface area of Earth

The surface area AA of a sphere is given by the formula:

A=4πr2A = 4\pi r^2

Given:

  • Radius r=6400r = 6400 km

Let's calculate the surface area of Earth.

Part (b): Area of Earth's surface covered with water

If 70% of Earth's surface is covered with water, the area covered by water can be calculated as:

Water Area=0.7×Total Surface Area\text{Water Area} = 0.7 \times \text{Total Surface Area}

Part (c): Area of Earth's surface that is land

The area of Earth's surface that is land is simply the remaining 30% of the total surface area:

Land Area=0.3×Total Surface Area\text{Land Area} = 0.3 \times \text{Total Surface Area}

Let's calculate these values now.Here are the results:

(a) The surface area of Earth is approximately 514,718,540 square kilometers, rounded to the nearest 10 square kilometers.

(b) The area of Earth's surface covered with water is approximately 360,302,980 square kilometers.

(c) The area of Earth's surface that is land is approximately 154,415,560 square kilometers.

Would you like to dive deeper into any of these calculations or have any further questions?

Here are five related questions you might find interesting:

  1. How does the surface area of Earth compare to that of other planets in our solar system?
  2. What is the volume of Earth if we consider it as a sphere?
  3. How would the surface area change if Earth's radius were 1% larger?
  4. How can you calculate the circumference of Earth using its radius?
  5. If Earth's surface area were 80% water, what would the land area be?

Tip: Understanding the proportions of water and land on Earth's surface can be critical for studies in geography, environmental science, and climate change analysis.

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Math Problem Analysis

Mathematical Concepts

Geometry
Spheres
Percentages

Formulas

Surface area of a sphere: A = 4πr^2

Theorems

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Suitable Grade Level

Grades 9-12