Math Problem Statement

What is the volume of this sphere? the radius is 36

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

Solution

The volume VV of a sphere is given by the formula:

V=43πr3V = \frac{4}{3} \pi r^3

where rr is the radius of the sphere and π\pi is approximately 3.14.

Given that r=36r = 36, we can plug this into the formula:

V=43×3.14×(36)3V = \frac{4}{3} \times 3.14 \times (36)^3

First, calculate 36336^3:

363=36×36×36=46,65636^3 = 36 \times 36 \times 36 = 46,656

Now, plug this value back into the formula:

V=43×3.14×46,656V = \frac{4}{3} \times 3.14 \times 46,656

Calculate the result step by step:

V=43×146,497.92=4×146,497.923=585,991.683=195,330.56V = \frac{4}{3} \times 146,497.92 = \frac{4 \times 146,497.92}{3} = \frac{585,991.68}{3} = 195,330.56

So, the volume of the sphere is approximately 195,330.56 cubic units.

Do you have any questions or want further details?

Here are 5 related questions to expand on this:

  1. How does the formula for a sphere's volume compare to that of a cylinder?
  2. How would the volume change if the radius was doubled?
  3. Can you derive the volume formula for a sphere using calculus?
  4. How would using a more accurate value for π\pi affect the result?
  5. What would be the surface area of this sphere?

Tip: Always calculate exponents before multiplying by other terms in a formula for best accuracy.

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Math Problem Analysis

Mathematical Concepts

Geometry
Volume of a Sphere

Formulas

V = (4/3) π r^3

Theorems

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Suitable Grade Level

Grades 8-10