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The radius of the base of a cylinder is 10 centimeters, and its height is 20 centimeters. A cone is used to fill the cylinder with water. The radius of the cone's base is 5 centimeters, and its height is 10 centimeters.

The number of times one needs to use the completely filled cone to completely fill the cylinder with water is.....

Verified Answer :

chancedale

Im like 90% sure that your answer should be 2.

Answer:

24 times.

Step-by-step explanation:

Since, the volume of a cone,

\(V=\frac{1}{3}\pi r^2 h\)

While, the volume of a cylinder,

\(V=\pi r^2 h\)

Where, r = radius,

h = height,

Thus, the volume of the cone having radius 5 cm and height 10 cm,

\(V_1=\frac{1}{3}\pi (5)^2(10)\)

And, the volume of the cylinder having radius 10 cm, and 20 cm,

\(V_2=\pi (10)^2 (20)\)

Hence, the number of times we need to use cone to completely fill the cylinder = \(\frac{V_2}{V_1}\)

\(=\frac{\pi (10)^2 (20)}{\frac{1}{3}\pi (5)^2(10)}\)

\(=\frac{2000}{250/3}\)

\(=\frac{6000}{250}\)

\(=24\)

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