**volume**of the given

**cone**with

**14 inches**in

**height**and

**10 inches in diameter**as shown in Figure 1. The question depends on the

**cone geometry.**A

**cone**is a

**3D solid shape**with a

**circular body**at the bottom and a

**triangular shape**towards the

**top.**The

**volume**of the

**cone**can be calculated by the formula given below: \[ Volume\ V = \dfrac{ 1 }{ 3 } \pi r^2 h \] Here, \[ r = Radius\ of\ the\ circular\ body\ of\ the\ cone \] \[ h = Height\ of\ the\ cone \]

## Expert Answer

The given information about the question is as follows: \[ Diameter\ d = 10\ in \] \[ Height\ h = 14\ in \] To find the**radius**of the

**cone,**we

**divide**the

**diameter**in

**half**to calculate its

**radius,**which is given as: \[ r = \dfrac{ d }{ 2 } \] \[ r = \dfrac{ 10 }{ 2 } \] \[ r = 5\ in \] The formula for the

**volume**of the

**cone**is given as: \[ Volume\ V = \dfrac{ 1 }{ 3 } \pi r^2 h \] Substituting the values, we get: \[ V = \dfrac{ 1 }{ 3 } \pi \times (5)^2 \times 14 \] \[ V = \dfrac{ 1 }{ 3 } \pi \times 25 \times 14 \] \[ V = \dfrac{ 1 }{ 3 } 350 \pi \] \[ V = 116.67 \pi \] \[ V = 366.52 {in}^3 \]

## Numerical Result

The**volume**of the

**cone**with

**10 inches**in

**diameter**and

**14 inches**in

**height**is calculated to be: \[ V = 366.52 {in}^3 \]

## Example

Find the**volume**of the given

**cone**below with

**12 inches**in

**diameter**and

**10 inches in height.**\[ Height\ h = 10\ in \] \[ Diameter\ d = 12\ in \] In order to calculate the

**radius**of the

**cone,**we divide the

**diameter**in

**half**to calculate its

**radius,**which is given as: \[ r = \dfrac{ d }{ 2 } \] \[ r = \dfrac{ 12 }{ 2 } \] \[ r = 6\ in \] The formula for the

**volume**of the

**cone**is given as: \[ Volume\ V = \dfrac{ 1 }{ 3 } \pi r^2 h \] Substituting the values, we get: \[ V = \dfrac{ 1 }{ 3 } \pi \times (6)^2 \times 10 \] \[ V = \dfrac{ 1 }{ 3 } \pi \times 36 \times 10 \] \[ V = \dfrac{ 1 }{ 3 } 360 \pi \] \[ V = 120\pi \] \[ V = 377 {in}^3 \]

*Images/Mathematical Drawings are created with Geogebra.*

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