Question

Help me find the volume of the composite figure

Answer 1

Answer:

$V = 97.911in^3$

Step-by-step 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:

$V_2 = \frac{\pi r^2h}{3}$

Where

h = 5.1

$r = \frac{1}{2} * Diameter$

$r = \frac{1}{2} * 5.1$

$r = 2.55$

So, we have:

$V_2 = \frac{\pi r^2h}{3}$

$V_2 = \frac{\pi * 2.55^2 * 5.1}{3}$

$V_2 = \frac{22 * 2.55^2 * 5.1}{7*3}$

$V_2 = \frac{729.5805}{21}$

$V_2 = 34.74$

The volume of the figure is:

$V=V_1 - V_2$

$V_1 = 132.651$

$V = 132.651 - 34.74$

$V = 97.911in^3$