To find how much more the new cans will hold after increasing the dimensions by a multiple of 1.12, we first need to determine the new dimensions and then calculate the new volume of the cans.
Given dimensions of the current can:
- Height (h) = 12 cm
- Diameter (d) = 6 cm
- Radius (r) = diameter / 2 = 6 cm / 2 = 3 cm
The new dimensions will be:
- New height (h') = 12 cm × 1.12 = 13.44 cm
- New diameter (d') = 6 cm × 1.12 = 6.72 cm
- New radius (r') = d' / 2 = 6.72 cm / 2 = 3.36 cm
Next, we calculate the new volume (V') of the can using the formula for the volume of a cylinder: \[ V = \pi r^2 h \] Using \( \pi \approx 3.14 \): \[ V' = 3.14 \times (3.36)^2 \times 13.44 \]
Calculating \( (3.36)^2 \): \[ (3.36)^2 = 11.296 \]
Now substituting back into the volume formula: \[ V' = 3.14 \times 11.296 \times 13.44 \]
Calculating \( 3.14 \times 11.296 \): \[ 3.14 \times 11.296 \approx 35.43 \]
Now multiply that by 13.44: \[ V' \approx 35.43 \times 13.44 \approx 476.44 cm^3 \]
The original volume of the can is given as 339.12 cm³. Now, we find how much more the new can holds: \[ \text{Increase in volume} = V' - V = 476.44 - 339.12 \] \[ \text{Increase in volume} \approx 137.32 cm^3 \]
Therefore, the new cans will hold 137.32 cm³ more.
So the answer is:
137.32 cm³
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