The change in surface area of a spherical balloon (ΔSA) in terms of the change in radius (Δr) is best expressed as ΔSA=4π(r2+r1)Δr, where r1 and r2 are the initial and final radii of the sphere.
To answer the question about the change in surface area (ΔSA) of a spherical balloon in terms of the change in radius (Δr), we will need to use the formula for the surface area of a sphere, which is SA=4πr².
If we consider two radii, r1 and r2, with r2 being slightly larger due to inflation, the new surface area will be SA2=4πr2², and the original surface area is SA1=4πr1².
The change in surface area is ΔSA=SA2-SA1.
When we substitute the expressions for SA2 and SA1 into ΔSA and simplify, we find that:
ΔSA = 4π(r2² - r1²) = 4π(r2 + r1)(r2 - r1) = 4π(r2 + r1)Δr
Since r2 - r1 is the change in the radius (Δr), the expression for the change in surface area in terms of Δr is:
ΔSA = 4π(r2 + r1)Δr
Therefore, the correct option is c) ΔSA=4π(r2+r1)Δr.