complete the statements about the cone. the height is units. the radius is units. the volume is π cubic units.
complete the statements about the cone. the height is units. the radius is units. the volume is π cubic units.
Answer
Explanation:
Step1: Identify the height
The height of the cone is the perpendicular distance from the vertex to the base. Here, the height $h = 6$ units.
Step2: Find the radius using the Pythagorean theorem
The slant - height $l = 10$ and height $h = 6$. By the Pythagorean theorem $l^{2}=h^{2}+r^{2}$, so $r=\sqrt{l^{2}-h^{2}}=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8$ units.
Step3: Calculate the volume of the cone
The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 8$ and $h = 6$ into the formula: $V=\frac{1}{3}\pi\times8^{2}\times6=\frac{1}{3}\pi\times64\times6 = 128\pi$ cubic units.
Answer:
The height is 6 units. The radius is 8 units. The volume is 128π cubic units.