To find out which container holds more ice cream, we'll calculate the volume of both the cone and the cup.
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Volume of the Cone:
The formula for the volume \( V \) of a cone is given by: \[ V = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.- The cone has a height \( x = 6 \) in and a radius \( w = 4 \) in.
- Plugging in the values: \[ V_{cone} = \frac{1}{3} \times 3.14 \times (4)^2 \times 6 \] \[ V_{cone} = \frac{1}{3} \times 3.14 \times 16 \times 6 \] \[ V_{cone} = \frac{1}{3} \times 3.14 \times 96 \] \[ V_{cone} = \frac{301.44}{3} \] \[ V_{cone} \approx 100.48 , \text{in}^3 \]
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Volume of the Cup (Cylinder):
The formula for the volume \( V \) of a cylinder is given by: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height.- The diameter of the cup \( y = 6 \) in, so the radius \( r \) is half of that: \( r = \frac{6}{2} = 3 \) in.
- The height of the cup \( z = 2 \) in.
- Plugging in the values: \[ V_{cup} = 3.14 \times (3)^2 \times 2 \] \[ V_{cup} = 3.14 \times 9 \times 2 \] \[ V_{cup} = 3.14 \times 18 \] \[ V_{cup} = 56.52 , \text{in}^3 \]
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Comparison of Volumes:
- Volume of Cone: \( V_{cone} \approx 100.48 , \text{in}^3 \)
- Volume of Cup: \( V_{cup} = 56.52 , \text{in}^3 \)
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Finding the Difference:
- To find how much more the cone holds than the cup: \[ V_{cone} - V_{cup} \approx 100.48 - 56.52 \approx 43.96 , \text{in}^3 \]
Therefore, the cone holds 43.96 in³ more ice cream than the cup.
So the correct answer is: The cone holds 43.96 in³ more ice cream than the cup.