Math Problem Statement

The radius, R, of a sphere is 7.9 mm. Calculate the sphere's volume, V. Use the value 3.14 for π, and round your answer to the nearest tenth.

Solution

To solve for the volume VV of a sphere, we can use the formula:

V=43πR3V = \frac{4}{3} \pi R^3

Given:

  • Radius R=7.9mmR = 7.9 \, \text{mm}
  • π=3.14\pi = 3.14

Let's calculate the volume using these values.

I will now compute it.The volume of the sphere is approximately 2064.2mm32064.2 \, \text{mm}^3, rounded to the nearest tenth.

Do you have any questions, or would you like further details on the solution?

Here are 5 related questions to expand your understanding:

  1. How does changing the radius affect the volume of a sphere?
  2. What would be the volume if the radius were doubled?
  3. Can you derive the formula for the surface area of a sphere?
  4. How does the use of a more accurate value for π\pi (e.g., 3.14159) affect the calculation?
  5. What is the relationship between the volume of a sphere and the volume of a cylinder with the same radius and height?

Tip: When solving geometry problems involving π\pi, keeping more digits for intermediate steps can improve accuracy in final answers.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of a Sphere

Formulas

V = (4/3)πR³

Theorems

Volume of a sphere

Suitable Grade Level

Grades 7-10