The diameters of the two circular ends of a bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is:

Given:
Height, h = 35 cm
Diameter of larger end, D = 44 cm
Diameter of smaller end, d = 24 cm
Radii:
Larger radius, $$R = \dfrac{D}{2} = \dfrac{44}{2} = 22$$​ cm
Smaller radius, $$r = \dfrac{d}{2} = \dfrac{24}{2} = 12$$​cm
Formula used:
Volume of frustum of a cone:
​$$V = \dfrac{1}{3} \pi h (R^2 + r^2 + Rr)$$​​
Solution:
​$$V = \dfrac{1}{3} \times \dfrac{22}{7} \times 35 \times (22^2 + 12^2 + 22 \times 12)\\ \ \\= \dfrac{1}{3} \times \dfrac{22}{7} \times 35 \times (484 + 144 + 264)\\ \ \\= \dfrac{1}{3} \times \dfrac{22}{7} \times 35 \times 892\\ \ \\= \dfrac{1}{3} \times 110 \times 892\\ \ \\= \dfrac{98120}{3} \, \text{cm}^3\\V \approx 32706.67 \, \text{cm}^3$$​​
Capacity in litres:
​$$1 litre = 1000 cm^3$$​​
Capacity $$= \dfrac{32706.67}{1000} = 32.7067$$​ litre
Therefore, the capacity of the bucket is approximately 32.7 litre.
Correct answer: (d) 32.7 litre