Question

Help me find the volume of the composite figure

Answer 1

`V = 97.911in^3`

Explanation:

Given

Shapes: Cube and Cone

Required

Determine the volume

First we calculate the volume of the cube

`V_1 = l^3`

Where

l = side length = 5.1

`V_1 = 5.1^3`

`V_1 = 132.651`

Next, calculate the volume of the cone using:

`V_2 = (\pi r^2h)/(3)`

Where

h = 5.1

`r = (1)/(2) * Diameter`

`r = (1)/(2) * 5.1`

`r = 2.55`

So, we have:

`V_2 = (\pi r^2h)/(3)`

`V_2 = (\pi * 2.55^2 * 5.1)/(3)`

`V_2 = (22 * 2.55^2 * 5.1)/(7*3)`

`V_2 = (729.5805)/(21)`

`V_2 = 34.74`

The volume of the figure is:

`V=V_1 - V_2`

`V_1 = 132.651`

`V = 132.651 - 34.74`

`V = 97.911in^3`