Question

determining the volume of a cone
complete the statements about the cone.
the height is \boxed{} units.
the radius is \boxed{} units.
the volume is \boxed{}pi cubic units.

Explanation:

Step1: Identify the height

The dashed line with length 6 is marked as perpendicular to the base center, so this is the height.
Height $h = 6$ units

Step2: Calculate the radius

Use Pythagorean theorem: $r = \sqrt{l^2 - h^2}$, where $l=10$ (slant height), $h=6$.
$r = \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8$ units

Step3: Compute the cone volume

Use volume formula $V = \frac{1}{3}\pi r^2 h$.
$V = \frac{1}{3}\pi \times 8^2 \times 6 = \frac{1}{3}\pi \times 64 \times 6 = 128\pi$ cubic units

Answer:

The height is 6 units.
The radius is 8 units.
The volume is 128$\pi$ cubic units.