Bucket Capacity Calculation:

To determine the capacity of the bucket, we need to find the volume of the shape formed by the bucket. Since the bucket has a cylindrical shape, we can calculate its volume using the formula for the volume of a cylinder.

Volume of a Cylinder:
The volume of a cylinder is given by the formula V = πr^2h, where V represents volume, r represents the radius of the base, and h represents the height of the cylinder.

Determining the Radii and Height:
Given that the radii of the ends of the bucket are 16 cm and 11 cm, and the height of the bucket is 42 cm, we can use these values to calculate the bucket's capacity.

Calculating the Volume:
Using the formula for the volume of a cylinder, we can substitute the given values into the equation to find the volume.

V = πr^2h

For the larger end of the bucket:
radius (r1) = 16 cm
height (h) = 42 cm

V1 = π(16 cm)^2(42 cm)

For the smaller end of the bucket:
radius (r2) = 11 cm
height (h) = 42 cm

V2 = π(11 cm)^2(42 cm)

Calculating the Capacity:
To find the bucket's capacity, we need to subtract the volume of the smaller end from the volume of the larger end. This will give us the volume of the shape formed by the bucket.

Capacity = V1 - V2

Final Answer:
By substituting the values into the equations and performing the calculations, we can find the capacity of the bucket.

24332 cubic centimetres.