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On the right is a scaled diagram of the Leaning Tower of Pisa - Junior Cycle Mathematics - Question 1 - 2018
Question 1
On the right is a scaled diagram of the Leaning Tower of Pisa. (a) Measure the width and the vertical height of the tower, marked A and B on the diagram. Give each ... show full transcript
Worked Solution & Example Answer:On the right is a scaled diagram of the Leaning Tower of Pisa - Junior Cycle Mathematics - Question 1 - 2018
Step 1
(a) Measure the width and the vertical height of the tower.
Answer
To find the measurements:
- Width Measurement: From the diagram, measure the width marked A which is found to be 3 cm.
- Height Measurement: Measure the vertical height marked B, found to be 11 cm.
Final Answers:
- A = 3 cm
- B = 11 cm
Step 2
(b) Use this fact to work out the actual width and actual vertical height of the tower.
Answer
Given the scale of 1 cm = 5 m:
-
Actual Width Calculation:
Actual Width = 3 cm × 5 m/cm = 15 m
-
Actual Height Calculation:
Actual Height = 11 cm × 5 m/cm = 55 m
Final Answers:
- Actual width = 15 m
- Actual vertical height = 55 m
Step 3
(c) Use Claire’s estimate to work out the volume of the original tower.
Answer
To calculate the volume of a cylinder, we use the formula:
Where:
- Radius, r = 7 m
- Height, h = 60 m
Plugging in the values: Using π ≈ 3.14:
Rounding to one decimal place: Final Answer:
- Volume of the original tower = 9236.2 m³