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VolLab
A third of the cylinder that contains it.
A cone's volume is always exactly one-third of the cylinder that shares its base and height — a relationship you can verify by filling a cone-shaped cup with water and pouring it into a same-sized cylinder three times.
The height is the straight perpendicular line from apex to base center; the slant height (used for surface area) runs along the cone's outer surface, and is always longer — found via the Pythagorean theorem.
Volume
150.796
What you entered
Volume = ⅓ × π × r² × h
(1/3) × π × 4² × 9= 150.7964Slant height
√(4² + 9²)= 9.8489Total surface area = πr(r + slant)
π × 4 × (4 + 9.8489)= 174.0299Result
Volume: 150.796
A cone with radius 4 and height 9 has a volume of 150.796 and a total surface area of 174.03.