Number limits, overflow, and roundoff

A scientist is running a program to calculate the volume of a cone:

radius ← 17.24
height ← 5.24
volume ← PI * (radius * radius) * (height / 3)

The code relies on the built-in constant PI. After running the code, the variable volume stores 1630.9266447568566.

Their supervisor checks their results by running the same calculation on their own computer. Their program results in a volume of 1630.9266447564448.

The two values are very close, but not quite the same.

Which of these is the most likely explanation for the difference?

(Choice A)
One of the computers has a bug in its mathematical operations.
(Choice B)
The two computers executed the arithmetic operations using a different order of operations.
(Choice C)
One computer used an integer representation for the numbers while the other computer used the more accurate floating-point representation.
(Choice D)
The two computers represent the constant PI with a different level of precision, due to their rounding strategy or size limitations.
(Choice E)
One of the computers experienced an integer overflow error when calculating the result.

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This code is written in pseudocode. You can't actually run pseudocode, but we use it for planning programs and for thinking about code independently of specific programming language.

AP CSP exam questions use pseudocode, so it's helpful to become familiar with it.

Here is a reference for the pseudocode used here:

Instruction	Explanation
`a ← expression`	Evaluates `expression` and assigns the result to the variable `a`.
`a + b`	Evaluates to the result of `b` added to `a`
`a - b`	Evaluates to the result of `b` subtracted from `a`
`a * b`	Evaluates to the result of `a` multiplied by `b`
`a / b`	Evaluates to the result of `a` divided by `b`
a `MOD` b	Evaluates to the remainder when a is divided by b. Assumes that `a` and `b` are positive integers.

Computers and the Internet

Course: Computers and the Internet > Unit 1

Problem