The radius of a sphere was measured to be 12 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer. The surface area of a sphere is 5:47:1'2 .) 2 H cm What is the relative error? (Round your answer to three decimal places.) H (b) Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer. The volume of a sphere is V=%m3 .) 3 H crn What is the relative error? (Round your answer to three decimal places.) H Suppose that we don't have a formula for 900 but we know that 9(2) = 5 and g'[x) = l/ x2 + 5 for all X. Use a linear approximation to estimate g(1.99) and g(2.01). mm: mm