Question

find the volume of this object. use 3 for π. volume of the cylinder v ≈ 576 cm³ volume of a cone v = \frac{\pi r^{2}h}{3} now lets calculate the volume of the cone. v = \frac{\pi ?^{2} }{3} hint: plug in the value of the radius. the diameter is 8. the radius is half this value.

Explanation:

Step1: Find the radius of the cone

The diameter of the cone is 8 cm. The radius $r$ is half of the diameter, so $r=\frac{8}{2}=4$ cm.

Step2: Identify the height of the cone

The height of the cone $h = 10$ cm.

Step3: Calculate the volume of the cone

Using the formula $V=\frac{\pi r^{2}h}{3}$, and substituting $\pi = 3$, $r = 4$ cm and $h=10$ cm, we get $V=\frac{3\times4^{2}\times10}{3}$. First, calculate $4^{2}=16$. Then $3\times16\times10 = 480$. Dividing by 3 gives $V = 160$ $cm^{3}$.

Step4: Calculate the total volume of the object

The volume of the cylinder is 576 $cm^{3}$ and the volume of the cone is 160 $cm^{3}$. The total volume $V_{total}=576 + 160=736$ $cm^{3}$.

Answer:

$736$ $cm^{3}$