Question

Find the length of the height of the cone.

(1 point)

Answer 1

I don't have the rest of the problem (numbers or a diagram). Could you paste the full problem or upload the figure?

Meanwhile, here are the common ways to get the height h of a (right circular) cone — if any of these match what you were given, plug in the values:

- If you know the slant height l and base radius r:
h = sqrt(l^2 − r^2).

- If you know the volume V and the base radius r:
V = (1/3)π r^2 h ⇒ h = 3V / (π r^2).

- If you know the lateral (curved) surface area A_l and r:
A_l = π r l ⇒ l = A_l/(π r) ⇒ h = sqrt(l^2 − r^2) = sqrt((A_l/(π r))^2 − r^2).

- If the cone is inscribed in a sphere of radius R (vertex and base circle on the sphere) and base radius r:
using (h − R)^2 + r^2 = R^2 ⇒ h = R ± sqrt(R^2 − r^2). (Choose the sign appropriate to the cone’s position; for the usual cone with apex at one pole and base inside the sphere, h = R + sqrt(R^2 − r^2).)

Tell me which quantities you have (or share the picture) and I’ll compute h.