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Question 11
Fiona finds the volumes of five different cylinders. Each of them has a height of K centimetres. (a) Complete the table below to show the volume of each of the five... show full transcript
Step 1
Answer
To find the volume of a cylinder, we use the formula:
where:
Using this formula, we can fill in the missing volumes for the cylinders:
For radius = 1 cm:
For radius = 2 cm:
For radius = 3 cm (given):
For radius = 4 cm:
For radius = 5 cm:
Thus, the completed table is:
Radius of cylinder (cm) | Height of cylinder (cm) | Volume of cylinder (cm³) |
---|---|---|
1 | K | πK |
2 | K | 4πK |
3 | K | 9πK |
4 | K | 16πK |
5 | K | 25πK |
Step 2
Answer
The sequence of volumes is:
By observing the coefficients: 1, 4, 9, 16, 25, we can see that these correspond to the square of the integers:
The first difference is:
And the second difference is constant:
Since the second difference is constant, the sequence is quadratic.
Answer: The sequence is quadratic.
Justification: The volumes follow a pattern where each term is the square of the radius multiplied by , indicating a quadratic relationship.
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