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  • The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is (A) 32.7 litres

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

(A) 32.7 litres              (B) 33.7 litres              (C) 34.7 litres              (D) 31.7 litres

Answers (1)

Answer(A) 32.7 litres

Solution

            Volume of frustum of cone =\frac{\pi h}{3} (r_{1}^{2}+ r_{2}^{2}+r_{1}r_{2})

            Diameter of first end = 44 cm

            Radius (r_{1})=\frac{44}{2}=22cm

            Diameter of second end = 24 cm

            Radius (r_{2})=\frac{24}{2}=12cm

            Height (h) = 35cm

            Volume =\frac{\pi h}{3} (r_{1}^{2}+ r_{2}^{2}+r_{1}r_{2})

                        =\frac{22 \times 35}{7 \times 3}(22^{2}+12^{2}+22 \times 12)

                        = \frac{110}{3}[484 +144+264]

                        = \frac{110}{3}[892]

                        = 32706.67 cm^{3}

            We know that 1 liter = 1000 cm3

            \therefore 32706.67 cm^{3} =32.7 l

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