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:
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:
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 = 3.1425^2 10/3=261.8 cm^3
Number of times required = volume of cylinder /volume of cone
6283/261.8 =24 times