Answer:
[tex]V=16,594.15 ft^{3}[/tex]
Step-by-step explanation:
The volume of a cylinder is defined as
[tex]V= \pi r^{2} h[/tex]
So, by given we know that the diameter of the circular base is [tex]1 \frac{2}{5}[/tex] times its height which is [tex]19 \frac{3}{4}ft[/tex], if we transform each mixed number into a fraction, it would ne
Diameter: [tex]\frac{7}{5}[/tex] times the height.
Height: [tex]\frac{79}{4}ft[/tex]
That means,
[tex]d=\frac{7}{5} h[/tex], replacing the height, we have
[tex]d=\frac{7}{5}(\frac{79}{4} ) \\d=\frac{553}{20}[/tex]
But, the radius is half the diameter by definition
[tex]r=\frac{d}{2}=\frac{\frac{553}{20} }{2}}=\frac{553}{40} \\r=13\frac{33}{40}ft[/tex]
Now that we know the radius and the height, we can use the formula to find the volume
[tex]V= \pi r^{2} h\\V= (3.14)(\frac{553}{40} )^{2}(\frac{553}{20}} )\\ V=16,594.15 ft^{3}[/tex]
Therefore, the volume rounded to the nearest hundred is
[tex]V=16,594.15 ft^{3}[/tex]
