Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 c m and radius of top as 2.5 c m and is full of water. Metallic spherical balls each of diameter 0.5 c m are put in the vessel due to which \left(\right. \frac{2}{5} \left.\right)th of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

Foundation

Mathematics Foundation

Surface Area and Volume

Cone

Sphere

Question

Sushant has a vessel, of the form of an inverted cone, open at the top, of height

11 c m

and radius of top as

2.5 c m

and is full of water. Metallic spherical balls each of diameter

0.5 c m

are put in the vessel due to which

(\frac{2}{5})

th of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

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Given

h = 11 c m, r_{1} = 2.5 c m, r_{2} = 0.25 c m

25 \times

volume of cone

= n \times

Volume of each spherical ball

25 \times \frac{1}{3} π r_{1}^{2} h = n \times \frac{4}{3} π r_{2}^{3}

r_{1}^{2} h = n \times 10 r_{2}^{3}

2. 5^{2} \times 11 = n \times 10 (0.2 5^{3})

n = 440