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

Answer:

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

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' = $\frac{1}{3}\pi r'^2h'$...(2)

$\frac{V}{V'}=\frac{\pi r^2h}{\frac{1}{3}\pi r'^2h'}$

$\frac{V}{V'}=\frac{3.14\times 10 cm\times 10 cm\times 20 cm}{\frac{1}{3}\times 3.14\times 5 cm \times 5 cm\times 10}$

$\frac{V}{V'}=24$

V = 24V'

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

Answer 2

Answer:

24

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