Find the approximate increase in surface area of a sphere of it radius increases from 4cm to 4.025cm

Answer 1

To find the increase in surface area, we first need to calculate the surface area of the sphere with a radius of 4cm and then with a radius of 4.025cm.

The formula for the surface area of a sphere is:
Surface Area = 4πr^2

For a radius of 4cm:
Surface Area = 4 * π * (4)^2
Surface Area = 4 * π * 16
Surface Area = 64π

For a radius of 4.025cm:
Surface Area = 4 * π * (4.025)^2
Surface Area = 4 * π * 16.200625
Surface Area = 64.8025π

The increase in surface area is:
Increase = 64.8025π - 64π
Increase = 0.8025π

Approximating π to 3.14:
Increase ≈ 0.8025 * 3.14
Increase ≈ 2.52155 cm^2

Therefore, the approximate increase in surface area is 2.52 cm^2.