Question

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

Answer 1

24

Step-by-step explanation:

Volume of a cylinder =
`\pi`r^2h

Radius of cylinder = 10cm

Height of cylinder = 20cm

Volume = 3.142*(10^2)*20 =6,283cm^3

Volume of a cone =
`\pi`r^2h/3

Radius of cone = 5cm

Height of cone = 10cm

Volume = 3.142*5^2 *10/3=261.8 cm^3

Number of times required = volume of cylinder /volume of cone

6283/261.8 =24 times

Answer 2

The number of times one needs to use the completely filled cone to completely fill the cylinder with water is 24.

Step-by-step explanation:

Radius of cylinder = r = 10 cm

Height of cylinder = h = 20 cm

Volume of cylinder= V =
`\pi r^2h`...(1)

Radius of the cone = r' = 5 cm

Height of cone = h' = 10 cm

Volume of cone = V' =
`(1)/(3)\pi r'^2h'`...(2)

`(V)/(V')=(\pi r^2h)/((1)/(3)\pi r'^2h')`

`(V)/(V')=(3.14* 10 cm* 10 cm* 20 cm)/((1)/(3)* 3.14* 5 cm * 5 cm* 10)`

`(V)/(V')=24`

V = 24V'

The number of times one needs to use the completely filled cone to completely fill the cylinder with water is 24.