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Asked: 2026-10-07T07:09:49+00:00 In:

The Earth’s surface has an estimated volume of 1.38 billion km³ of water. Suppose the Earth is a perfect sphere and all this water forms a uniform layer completely covering the Earth’s surface, like a thin water bubble. Estimate the thickness of this water layer. The Earth’s radius is ~6371 km. (i) Write an expression that gives the thickness of this water layer. (ii) Simplify the expression in (i) using a calculator.

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(i) Expression for thickness t is t ≈ V_water/(4πR²) or ∛(R³ + 3V/(4π)) − R. (ii) Surface area is 4π(6371)² ≈ 510,064,472 km². Dividing 1.38 × 10⁹ by this area gives thickness t ≈ 2.705 km (or ~2705 m).

Ganita Manjari Part 2 Class 9 Maths Chapter 14 Math of Space: Surface Area and Volume Solutions
Class 9 Maths Ganita Manjari Part 2 Chapter 14 Question Answer

1.38 billion km³ of wateran expression that gives the thickness of this waterearth’s surface has an estimated volumeganita manjari part 2 chapter 14 math of space surface area and volume solutionsganita manjari part 2 chapter 14 question answermath of space surface area and volume solutions – ganita manjari part ii chapter 14
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    1. (i) Since the water layer is extremely thin compared to Earth’s radius, its volume equals surface area multiplied by thickness: V ≈ 4πR²t, giving thickness expression t = V/(4πR²). The exact expression is t = ∛(R³ + 3V/(4π)) − R. (ii) Earth’s surface area is 4π(6371)² ≈ 5.10 × 10⁸ km². Evaluating t = 1.38 × 10⁹/(5.10 × 10⁸) ≈ 2.705 km, meaning the uniform water layer is approximately 2.71 kilometres thick.

       

      For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 14 Math of Space: Surface Area and Volume Question Answer (2026-27)

      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-14/

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