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Un cono mide 3 pulgadas de diámetro y tiene una capacidad de 12 pulgadas cúbicas de agua. Redondeada a la pulgada más cercana, ¿cuál es la altura del cono?

A. 1
B. 4
C. 5
D. 8

Answer :

We are given a cone with a diameter of 3 inches, so the radius is

[tex]$$
r = \frac{3}{2} = 1.5 \text{ inches.}
$$[/tex]

The volume of a cone is given by

[tex]$$
V = \frac{1}{3} \pi r^2 h.
$$[/tex]

Here, the volume is 12 cubic inches. Substituting the known values into the volume formula gives:

[tex]$$
12 = \frac{1}{3} \pi (1.5)^2 h.
$$[/tex]

First, calculate [tex]$(1.5)^2$[/tex]:

[tex]$$
(1.5)^2 = 2.25.
$$[/tex]

So the equation becomes:

[tex]$$
12 = \frac{1}{3} \pi \cdot 2.25 \cdot h.
$$[/tex]

To isolate [tex]$h$[/tex], multiply both sides by 3:

[tex]$$
36 = \pi \cdot 2.25 \cdot h.
$$[/tex]

Now, solve for [tex]$h$[/tex] by dividing both sides by [tex]$\pi \cdot 2.25$[/tex]:

[tex]$$
h = \frac{36}{\pi \cdot 2.25}.
$$[/tex]

Evaluating the right-hand side yields approximately:

[tex]$$
h \approx 5.092958 \text{ inches.}
$$[/tex]

Rounding to the nearest inch gives:

[tex]$$
h \approx 5 \text{ inches.}
$$[/tex]

Thus, the height of the cone is [tex]$\boxed{5}$[/tex] inches.

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