Question

what is the height of a cone if its radius length is 12 cm and its slant height is 39 cm?
cone height (h) = \boxed{} cm
round your length to the hundredths place.
(image of a cone with height h, radius 12 cm, slant height 39 cm)

Explanation:

Step1: Recall Pythagorean theorem for cone

In a right triangle formed by radius (\(r\)), height (\(h\)) and slant height (\(l\)) of a cone, \(l^{2}=r^{2}+h^{2}\). We need to solve for \(h\), so \(h = \sqrt{l^{2}-r^{2}}\).

Step2: Substitute values

Given \(r = 12\) cm and \(l = 39\) cm. Substitute into the formula: \(h=\sqrt{39^{2}-12^{2}}\). First, calculate \(39^{2}=1521\) and \(12^{2} = 144\). Then \(39^{2}-12^{2}=1521 - 144=1377\).

Step3: Calculate square root

Now, \(h=\sqrt{1377}\approx37.11\) (rounded to the hundredths place).

Answer:

\(37.11\)