Find the approximate increase in the surface area of a spherical balloon if it's radius increases from 4cm to 4.025cm

Answer 1

The surface area of a sphere is given by the formula A = 4πr^2, where r is the radius.

For the first scenario, when the radius is 4 cm:
A1 = 4π(4 cm)^2
A1 ≈ 201.06 cm^2

For the second scenario, when the radius is 4.025 cm:
A2 = 4π(4.025 cm)^2
A2 ≈ 204.05 cm^2

The approximate increase in surface area is:
ΔA ≈ A2 - A1
ΔA ≈ 204.05 cm^2 - 201.06 cm^2
ΔA ≈ 2.99 cm^2

Therefore, the approximate increase in surface area of the spherical balloon is 2.99 cm^2.