Math Problem Statement

Sphere: r=4cm

Solution

The image appears to contain handwritten mathematical content, with a particular focus on a sphere with a radius of 4 cm. Let's analyze the relevant information.

Given:

  • Sphere with radius r=4r = 4 cm

Common Calculations for a Sphere:

  1. Volume of the Sphere: V=43πr3V = \frac{4}{3} \pi r^3
  2. Surface Area of the Sphere: A=4πr2A = 4 \pi r^2

Let's calculate the volume and surface area using r=4r = 4 cm:

  1. Volume: V=43π(4)3=43π×64=2563π268.08cm3V = \frac{4}{3} \pi (4)^3 = \frac{4}{3} \pi \times 64 = \frac{256}{3} \pi \approx 268.08 \, \text{cm}^3

  2. Surface Area: A=4π(4)2=4π×16=64π201.06cm2A = 4 \pi (4)^2 = 4 \pi \times 16 = 64 \pi \approx 201.06 \, \text{cm}^2

These are the calculated volume and surface area of the sphere.

Would you like a more detailed explanation of these formulas or any other assistance?

Related Questions:

  1. How do you derive the formula for the volume of a sphere?
  2. How does the surface area formula for a sphere relate to its volume?
  3. What is the impact of doubling the radius on the sphere's volume and surface area?
  4. Can you apply these formulas to find the properties of a hemisphere?
  5. What are the real-life applications of calculating the volume and surface area of a sphere?

Tip: Always ensure to substitute the radius accurately in the formulas for volume and surface area to avoid errors in calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Sphere

Formulas

Volume of a Sphere
Surface Area of a Sphere

Theorems

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Suitable Grade Level

Grades 10-12