To calculate the amount of wax needed to make the crayon, we can model the crayon as a cylinder that tapers to a point (the tip). The volume of the crayon can be calculated by finding the volume of the cylinder and then subtracting the volume of the tip (which can be approximated as a cone).
Step 1: Calculate the volume of the cylindrical part of the crayon.
The formula for the volume of a cylinder is:
\[ V_{\text{cylinder}} = \pi r^2 h \]
where:
- \( r \) is the radius,
- \( h \) is the height (or length).
Given:
- \( r = 2 \) mm,
- The length of the crayon is \( 9 \) mm, which means the height of the cylindrical part is \( 9 \) mm - \( 6 \) mm (the tip) = \( 3 \) mm.
Calculating the volume of the cylindrical part:
\[ V_{\text{cylinder}} = 3.14 \times (2)^2 \times 3 = 3.14 \times 4 \times 3 = 3.14 \times 12 = 37.68 \text{ mm}^3 \]
Step 2: Calculate the volume of the conical tip of the crayon.
The formula for the volume of a cone is:
\[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \]
For the tip:
- \( r = 2 \) mm,
- \( h = 6 \) mm.
Calculating the volume of the conical tip:
\[ V_{\text{cone}} = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 = \frac{1}{3} \times 3.14 \times 4 \times 6 = \frac{1}{3} \times 3.14 \times 24 = \frac{75.36}{3} = 25.12 \text{ mm}^3 \]
Step 3: Calculate the total volume of the crayon.
Now, we find the total volume of the crayon by adding both volumes together:
\[ V_{\text{total}} = V_{\text{cylinder}} + V_{\text{cone}} = 37.68 + 25.12 = 62.8 \text{ mm}^3 \]
Step 4: Round the answer to the nearest whole number.
Rounding \( 62.8 \) to the nearest whole number gives us:
\[ \boxed{63} \text{ mm}^3 \]
Thus, the amount of wax needed to make the crayon is approximately \( 63 \text{ mm}^3 \).
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