How much water can an 8" diameter cylinder with a 10" stroke hold?

How much water can an 8" diameter cylinder with a 10" stroke hold?

• A. 251.2 cubic inches
• B. 502.4 cubic inches
• C. 314.0 cubic inches
• D. 628.0 cubic inches

Answer: (B)

To determine the volume of water the cylinder can hold, we need to calculate the volume of a cylinder using the formula: \[ \text{Volume} = \pi r^2 h \] In this case, the diameter of the cylinder is 8 inches. The radius is half of the diameter, so: \[ r = \frac{8\, \text{inches}}{2} = 4\, \text{inches} \] The stroke (height) of the cylinder is given as 10 inches. Now, substituting the radius and height into the volume formula: \[ \text{Volume} = \pi (4\, \text{inches})^2 (10\, \text{inches}) \] Calculating the radius squared: \[ (4\, \text{inches})^2 = 16\, \text{square inches} \] Now, substituting this back into the volume formula: \[ \text{Volume} = \pi (16\, \text{square inches})(10\, \text{inches}) = 160\pi\, \text{cubic inches} \] Using the approximation of \(\pi

To determine the volume of water the cylinder can hold, we need to calculate the volume of a cylinder using the formula:

[

\text{Volume} = \pi r^2 h

]

In this case, the diameter of the cylinder is 8 inches. The radius is half of the diameter, so:

[

r = \frac{8, \text{inches}}{2} = 4, \text{inches}

]

The stroke (height) of the cylinder is given as 10 inches. Now, substituting the radius and height into the volume formula:

[

\text{Volume} = \pi (4, \text{inches})^2 (10, \text{inches})

]

Calculating the radius squared:

[

(4, \text{inches})^2 = 16, \text{square inches}

]

Now, substituting this back into the volume formula:

[

\text{Volume} = \pi (16, \text{square inches})(10, \text{inches}) = 160\pi, \text{cubic inches}

]

Using the approximation of (\pi