Question
Marjorie needs to calculate how much water a cylindrical tank will hold. The tank is 9 feet high and has a diameter of 5 feet. Her work is shown below.
V = pi r squared h
Step 1: V = pi (2.5 squared) (9)
Step 2: V = pi (5) (9)
Step 3: V = (3.14) (5) (9)
Step 4: V = 141.3 cubic feet
What error did Marjorie make when calculating the volume of the tank?
In step 1, she substituted into the volume formula incorrectly.
In step 2, she calculated 2.5 squared incorrectly.
In step 3, the she substituted the wrong amount for Pi.
Marjorie correctly calculated the volume of the cylinder.
V = pi r squared h
Step 1: V = pi (2.5 squared) (9)
Step 2: V = pi (5) (9)
Step 3: V = (3.14) (5) (9)
Step 4: V = 141.3 cubic feet
What error did Marjorie make when calculating the volume of the tank?
In step 1, she substituted into the volume formula incorrectly.
In step 2, she calculated 2.5 squared incorrectly.
In step 3, the she substituted the wrong amount for Pi.
Marjorie correctly calculated the volume of the cylinder.
Answers
GPT-4o mini
Marjorie made an error in Step 2. After substituting the value in Step 1 (where she correctly calculated \(2.5\) squared, which is \(6.25\)), she should have multiplied \(6.25\) by \(9\) (the height) instead of incorrectly stating it as \(5\).
The correct calculation should be:
Step 1: \( V = \pi (2.5^2) (9) \)
Step 2: \( V = \pi (6.25) (9) \)
Step 3: \( V = \pi (56.25) \)
Step 4: \( V = (3.14) (56.25) \approx 176.625 \) cubic feet
So, the error is in Step 2, where she calculated and recorded \(2.5\) squared incorrectly, leading to the wrong subsequent calculations.
The correct calculation should be:
Step 1: \( V = \pi (2.5^2) (9) \)
Step 2: \( V = \pi (6.25) (9) \)
Step 3: \( V = \pi (56.25) \)
Step 4: \( V = (3.14) (56.25) \approx 176.625 \) cubic feet
So, the error is in Step 2, where she calculated and recorded \(2.5\) squared incorrectly, leading to the wrong subsequent calculations.