The radius of a sphere was measured to be 20cm with a a possible error of 1/5cm

Question

1).Use linear approximation to estimate the maximum error in the calculated surface area. Leave your answer in terms of pi.

2).Use linear approximation to estimate the maximum error in the calculated volume. Leave your answer in terms of pi.

Answer 1

you can use the same approach as for the paint on sphere.

A=4πr²
dA/dr=8πr
ΔA=8πr Δr
=8π(20)(1/5)
=32π