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A model of a volcano has a height of 12 in., and a diameter of 12 in. What is the volume of the model? Use 3.14 to approximate pi, and express your final answer as a decimal. Enter your answer in the box.

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A volcano is an inverted cone and with that, the volume can be solved through the equation,
                                       V = (1/3)(area of the base)(height)
We solve the area of the base first,
                       area of the base = (pi)(r²)
                                                    = 3.14(6 in)²
                                                    = 113.04 in²
Substituting these calculated values and the other givens above to the first equation,
                                         V = (1/3)(113.04 in²)(12 in) = 452.16 in³
Thus, the volume of the model is approximately equal to 452.16 in³.

Answer:  The answer is 452 cubic in.

Step-by-step explanation:  Given that a model of a volcano has a height of 12 in. and a diameter of 12 in.. We are to find the approximate volume of the model

Also, it is given to use that

[tex]\pi=3.14.[/tex]

Since a volcano is usually cone-shaped and we know that the volume of a cone with height 'h' and radius 'r' is given by

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

Here, r = 6 in. and h=12 in.

Therefore, the volume of the model will be

[tex]V=\dfrac{1}{3}\times3.14\times6^2\times12=\dfrac{1356.48}{3}=452.16\sim452~\textup{cubic. in.}[/tex]

Thus, the required volume will be 452 cubic. in.

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