Question

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.

Answer 1

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

`\pi=3.14.`

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

`V=(1)/(3)\pi r^2h.`

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

Therefore, the volume of the model will be

`V=(1)/(3)*3.14*6^2*12=(1356.48)/(3)=452.16\sim452~\textup{cubic. in.}`

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

Answer 2

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.