What is the maximum volume of a cylinder measuring 10 cm x 10 cm in stroke?

What is the maximum volume of a cylinder measuring 10 cm x 10 cm in stroke?

• A. 600 cm³
• B. 314 cm³
• C. 785 cm³
• D. 500 cm³

Answer: (C)

To find the maximum volume of a cylinder, you use the formula for the volume of a cylinder, which is: \[ V = \pi r^2 h \] where \( V \) is the volume, \( r \) is the radius of the base of the cylinder, and \( h \) is the height or stroke length. In this case, the cylinder has a height of 10 cm, and since the diameter is also 10 cm, the radius can be calculated as follows: \[ r = \frac{diameter}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm} \] Now substitute the radius and height into the volume formula: \[ V = \pi (5 \text{ cm})^2 (10 \text{ cm}) \] \[ V = \pi (25 \text{ cm}^2)(10 \text{ cm}) \] \[ V = 250\pi \text{ cm}^3 \] Using an approximate value for \( \pi \) as 3.14, we can calculate the volume: \[ V \approx 250 \times 3.14 = 785 \text{ cm}

To find the maximum volume of a cylinder, you use the formula for the volume of a cylinder, which is:

[ V = \pi r^2 h ]

where ( V ) is the volume, ( r ) is the radius of the base of the cylinder, and ( h ) is the height or stroke length.

In this case, the cylinder has a height of 10 cm, and since the diameter is also 10 cm, the radius can be calculated as follows:

[ r = \frac{diameter}{2} = \frac{10 \text{ cm}}{2} = 5 \text{ cm} ]

Now substitute the radius and height into the volume formula:

[ V = \pi (5 \text{ cm})^2 (10 \text{ cm}) ]

[ V = \pi (25 \text{ cm}^2)(10 \text{ cm}) ]

[ V = 250\pi \text{ cm}^3 ]

Using an approximate value for ( \pi ) as 3.14, we can calculate the volume:

[ V \approx 250 \times 3.14 = 785 \text{ cm}