⅓πr²h: Error Analysis & Misconceptions
Mathematics
Year 9
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the volume of cones using the formula ⅓πr²h, aimed at identifying common errors and misconceptions among Year 9 students.
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⅓πr²h: Error Analysis & Misconceptions
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Read the key concept carefully. The volume of a cone is given by ⅓πr²h, where r is the radius and h is the height. Pay attention to units and correct application of the formula.
B
Fluency & Practice
Answer the following questions to practice calculating the volume of cones using the formula ⅓πr²h.
1.
Calculate the volume of a cone with radius 4 cm and height 9 cm.
[2 marks]2.
A cone has radius 6 m and height 10 m. Find its volume in cubic meters.
[2 marks]3.
If the volume of a cone is 50π cm³ and its height is 10 cm, find the radius of the cone.
[3 marks]4.
Construct a cone with radius 3 cm and height 12 cm on the grid. Calculate its volume.
[3 marks]C
Problem Solving & Reasoning
Solve these multi-step problems and explain your reasoning clearly.
1.
A water tank is shaped like a cone with radius 5 m and height 8 m. Water is poured in to fill the tank to three-quarters of its capacity. Calculate the volume of water in cubic meters. Show your working.
[4 marks]2.
A conical paper cup has radius 3 cm and height 9 cm. If the cup is filled with juice, how much more juice is needed to fill it completely if it currently contains 60 cm³? Assume the cup is filled to half its height. Explain your steps.
[4 marks]D
Real-world Applications
Apply your understanding to real-world contexts.
1.
A conical flask has radius 7 cm and height 15 cm. It is filled with a liquid that has a density of 1.2 g/cm³. Calculate the mass of the liquid in grams.
[4 marks]E
Challenge & Extension
Tackle these more difficult problems to deepen your understanding.
1.
A cone and a cylinder have the same height of 10 m. The radius of the cone is 4 m, and the radius of the cylinder is 4 m. Which has a greater volume? Show your calculations and explain.
[3 marks]2.
A cone's volume is calculated incorrectly as πr²h without the ⅓ factor. How does this mistake affect the volume calculation? Provide an example with r=3 cm, h=9 cm, and correct the mistake.
[3 marks]F
Mixed Review
Answer these questions to review your understanding of ⅓πr²h.
1.
Plot the graph of y=⅓πr²h for r from 1 to 10 with h = 5 on the grid.
[3 marks]2.
Construct a cone with a radius of 5 units and height of 7 units on the grid. Calculate its volume and then double it. Show your working.
[4 marks]3.
Identify and correct the mistake in the following statement: 'To find the volume of a cone, multiply π by the radius squared, then multiply by the height and divide by 3.'
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet