Final answer:
The capacity of a frustum-shaped bucket is calculated using a special formula, and with the given dimensions, the volume is found to be 11765.76 cm³, which does not match any of the options provided in the question.
Step-by-step explanation:
To find the capacity of a bucket with different top and bottom radii, we need to use the volume formula for a frustum of a cone, not a cylinder because the radii are different. The formula for the volume of a frustum is given by:
V = (1/3) * π * h * (R2 + R * r + r2)
where:
- V = volume of the frustum
- h = height of the frustum
- R = radius of the larger circular base (top of the bucket)
- r = radius of the smaller circular base (bottom of the bucket)
Plugging in the given values:
V = (1/3) * 3.14 * 24 cm * (18 cm2 + 18 cm * 6 cm + 6 cm2)
We will calculate it step by step:
- Calculate the squared values and multiplication: 182 = 324 cm2, 62 = 36 cm2, 18 * 6 = 108 cm.
- Add these values: 324 + 108 + 36 = 468 cm2.
- Multiply by pi: 468 * 3.14 = 1470.72 cm2.
- Multiply by height (h): 1470.72 * 24 = 35297.28 cm3.
- Finally, divide by 3 to get the volume: 35297.28 / 3 = 11765.76 cm³.
Therefore, the capacity of the bucket is 11765.76 cm3, which is not listed in the given options. There might be an error in the question or the options provided.