Question

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

Answer 1

The answer is 24.

Explanation:

The volume of cylinder will be =
`V=\pi r^(2) h`

r = 10 cm

h = 20 cm

So, V =
`3.14*10*10*20=6280` cubic cm

The volume of cone will be =
`V=(1)/(3)* \pi r^(2) h`

r = 5 cm

h = 10 cm

So, V =
`(1)/(3)*3.14*5*5*10=261.67` cubic cm.

Now, the number of cones needed to fill the cylinder will be =
`6280/261.67=23.999` ≈ 24

The answer is 24.

Answer 2

Cylinder

Radius of the base of a cylinder=10 cm

Height = 20 cm

Cone

radius of the cone base= 5 cm

height = 10 cm

cone is used to fill the cylinder with water. Let n be the number of times the water in the cone is transferred in the cylinder to fill it completely.

A.T.Q

n × volume of cone = volume of cylinder

`n*\frac {1}{3}\pi R^(2) H=\pi r^(2)h`

Cancelling (π) from both sides,we get

⇒n×1/3×5×5×10=10×10×20

⇒n=[2000×3]÷250

n=24

24 cones having radius 5 cm and height 10 cm will fill the cylinder having radius of the base 10 centimeters, and height 20 centimeters.