whats the same volume of the cylinders; left cylinder h=2 d=3./ Right cylinder H=6 D=3

1 answer

To find the volume of each cylinder, we can use the formula for the volume of a cylinder:

\[ V = \pi r^2 h \]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height of the cylinder.

  1. Left Cylinder:

    • Height \( h = 2 \)
    • Diameter \( d = 3 \), so the radius \( r = \frac{d}{2} = \frac{3}{2} = 1.5 \)

    Now plug in the values:

    \[ V_{\text{left}} = \pi (1.5)^2 (2) = \pi (2.25)(2) = \pi (4.5) = 4.5\pi \]

  2. Right Cylinder:

    • Height \( H = 6 \)
    • Diameter \( D = 3 \), so the radius \( R = \frac{D}{2} = \frac{3}{2} = 1.5 \)

    Now plug in the values:

    \[ V_{\text{right}} = \pi (1.5)^2 (6) = \pi (2.25)(6) = \pi (13.5) = 13.5\pi \]

  3. Comparison:

    • Volume of the left cylinder: \( 4.5\pi \)
    • Volume of the right cylinder: \( 13.5\pi \)

The left and right cylinders do not have the same volume; the right cylinder has a volume that is three times that of the left cylinder. Specifically, the left cylinder has a volume of \( 4.5\pi \) cubic units, while the right cylinder has a volume of \( 13.5\pi \) cubic units.