Specialist2026 NHT Exam 2 Section A · Q3CAS active1 mark

Algorithm estimating a surface area of revolution

Consider the following algorithm to estimate the area of a certain surface of revolution.

define f(x)
  return √(x² + 1)
sum ← 0
left ← 0
while left ≤ 1
  area ← 2π × f((left + (left + 1))/2) × √((f(left) − f(left + 1))² + 1)
  sum ← sum + area
  left ← left + 1
end while
print sum

The algorithm above will print a value closest to

1 mark

7.604

14.662

22.265

24.765

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define f(x) return √(x² + 1) sum ← 0 left ← 0 while left ≤ 1 area ← 2π × f((left + (left + 1))/2) × √((f(left) − f(left + 1))² + 1) sum ← sum + area left ← left + 1 end while print sum