Respuesta :

volume of a cone: [tex] \frac{1}{3} \pi r^2h [/tex]
V=[tex] \frac{1}{3} * \pi *7.5^2*19=356.25 \pi [/tex]
My understanding is that to be exact, leave π as π, so the final answer is 356.25π in³

Answer:

[tex]V= \frac{1425}{4} \pi \\ V=1119[/tex]

Step-by-step explanation:

We must find the volume of a cone, that is a definite geometric figure and has the formula to find its volume.

Cone Volume Formula

[tex]V=\frac{\pi .r^2.h}{3}[/tex]

Data:

Height: 19 in

Diameter: 15-in

The diameter is twice the radius.

To find the radius of the cone we must divide the diameter by 2

[tex]r=\frac{15}{2}=7.5 in[/tex]

Now we apply the formula

[tex]V=\frac{\pi .(7.5)^2.(19)}{3}[/tex]

We can express the result more accurately leaving the value of pi or we can approximate it by rounding the decimals

[tex]V= \frac{1425}{4} \pi \\ V=1119[/tex]