Respuesta :
Answer:
The volume of the second cylinder is three times as large as the volume of the first cylinder .
Hence [tex]V_2=3\times V_1[/tex]
Step-by-step explanation:
Given that the height of one right circular cylinder is 6 centimeters and its radius is 3 centimeters.
Let [tex]h_1,r_1[/tex] be the height and radius of the first right circular cylinder respectively.
∴ [tex]h_1=6 cm[/tex] and [tex]r_1=3 cm[/tex]
The height of a second right circular cylinder is 18 centimeters and its radius is 3 centimeters.
Let [tex]h_2,r_2[/tex] be the height and radius of the second right circular cylinder respectively.
∴ [tex]h_1=18 cm[/tex] and [tex]r_1=3 cm[/tex]
To find the volume of the second cylinder is how many times as large as the volume of the first cylinder :
The formula for Volume of right circular cylinder is
[tex]V=\pi r^2h[/tex] units
The Volume of first right circular cylinder is
[tex]V_1=\pi r_1^2h_1[/tex]
Substitute the values in the formula we get
[tex]V_1=\pi (3^2)(6)[/tex]
[tex]V_1=\pi (9)(6)[/tex]
[tex]=54\pi [/tex] units
∴ [tex]V_1=54\pi [/tex] units
The Volume of second right circular cylinder is
[tex]V_2=\pi r_2^2h_2[/tex]
Substitute the values in the formula we get
[tex]V_2=\pi (3^2)(18)[/tex]
[tex]V_2=\pi (9)(18)[/tex]
[tex]=162\pi [/tex] units
∴ [tex]V_2=162\pi [/tex] units
From the volumes [tex]V_1 and V_2[/tex] we get
[tex]\frac{V_2}{V_1}=\frac{162\pi}{54\pi}[/tex]
[tex]=3[/tex]
[tex]\frac{V_2}{V_1}=3[/tex]
∴ [tex]V_2=3\times V_1[/tex]
