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Clive estimates the dimensions of a rectangular tank to be 5 m by 4 m by 3 m - Junior Cycle Mathematics - Question 9 - 2021
Question 9
Clive estimates the dimensions of a rectangular tank to be 5 m by 4 m by 3 m. (a) Use Clive’s values to work out the volume of the tank, in m². (b) Clive’s estimat... show full transcript
Worked Solution & Example Answer:Clive estimates the dimensions of a rectangular tank to be 5 m by 4 m by 3 m - Junior Cycle Mathematics - Question 9 - 2021
Step 1
a) Use Clive’s values to work out the volume of the tank, in m².
Answer
To find the volume of a rectangular tank, we use the formula:
where:
- is the length,
- is the width,
- is the height.
Using Clive's estimates:
- Length, m
- Width, m
- Height, m
Substituting the values:
Thus, the volume of the tank is 60 m³.
Step 2
b) Work out the largest value that K could have.
Answer
Clive's estimates are rounded to the nearest metre. Therefore:
- The length could be between 4.5 m and 5.5 m,
- The width could be between 3.5 m and 4.5 m,
- The height could be between 2.5 m and 3.5 m.
To maximize the volume, we will use the upper limits of these estimates:
- Maximum length = 5.5 m
- Maximum width = 4.5 m
- Maximum height = 3.5 m
Calculating the maximum volume:
Since K must be a natural number (K ∈ ℕ), the largest possible value of K is 86.