A cylinder with a diameter of 5 m and a height of 8 m is half full of liquid. What volume does the liquid occupy?

A cylinder with a diameter of 5 m and a height of 8 m is half full of liquid. What volume does the liquid occupy?

• A. 157.1 cubic cm
• B. 78.5 cubic cm
• C. 39.3 cubic cm
• D. 19.6 cubic cm

Answer: (B)

To find the volume of liquid that occupies the half-full cylinder, you first need to calculate the total volume of the cylinder and then halve it since the cylinder is stated to be half full. The formula for the volume of a cylinder is given by: \[ V = \pi r^2 h \] Where: - \( V \) is the volume, - \( r \) is the radius of the base of the cylinder, - \( h \) is the height of the cylinder, - \( \pi \) is approximately 3.14159. Given the diameter of the cylinder is 5 m, the radius \( r \) can be calculated as follows: \[ r = \frac{diameter}{2} = \frac{5\,m}{2} = 2.5\,m \] The height \( h \) of the cylinder is given as 8 m. Now, substituting these values into the formula for volume: \[ V = \pi (2.5\,m)^2 (8\,m) \] \[ V = \pi (6.25\,m^2) (8\,m) \] \[ V = \pi (50\,m^3) \] \[

To find the volume of liquid that occupies the half-full cylinder, you first need to calculate the total volume of the cylinder and then halve it since the cylinder is stated to be half full.

The formula for the volume of a cylinder is given by:

[ V = \pi r^2 h ]

Where:

• ( V ) is the volume,

• ( r ) is the radius of the base of the cylinder,

• ( h ) is the height of the cylinder,

• ( \pi ) is approximately 3.14159.

Given the diameter of the cylinder is 5 m, the radius ( r ) can be calculated as follows:

[ r = \frac{diameter}{2} = \frac{5,m}{2} = 2.5,m ]

The height ( h ) of the cylinder is given as 8 m. Now, substituting these values into the formula for volume:

[ V = \pi (2.5,m)^2 (8,m) ]

[ V = \pi (6.25,m^2) (8,m) ]

[ V = \pi (50,m^3) ]

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