Activity 2.7.20.
Constructing a cone.
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Materials NeededSheets of paper or cardboardScissors, glue/tape, and rulersA cylinder (e.g., cup or bottle) for comparison
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"How can we turn this into a cone?"Take a piece of paper and \(\textbf{cut a circle}\) any radius.
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\(\textbf{Cut out a sector and roll}\) the remaining part into a cone shape.
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Measure the radius and height of their cones.
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Calculate the volume using the formula .
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Equally, we can try this activity using; Empty Ice cream cones, A cylindrical cup of the \(\textbf{same height}\) and \(\textbf{base}\) as the cone and water.🔹 Steps:
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Fill the cone with water and pour it into the cylinder severally until the cylinder is full.
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How many cones of rice will fill the cylinder?
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\(\textbf{Notice that it takes exactly 3 full cones to fill the cylinder}\text{.}\)This is why the formula includes \(\frac{\textbf{1}}{\textbf{3}} \text{!}\)🔹 Mathematical Insight✔ This shows the formula:\begin{equation*} V_\text{cone} = \frac{1}{3} V_\text{cylinder} = \frac{1}{3} \pi r^2h \end{equation*}✔ The cone is one-third of the volume of a cylinder with the same base and height.
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