Question

question 6 of 10 the lateral surface area of cone a is exactly \\( \frac { 1 } { 2 } \\) the lateral surface area of cylinder b. a. true b. false

Explanation:

Step1: Recall the lateral surface area formulas

The lateral surface area of a cone \(S_{cone}=\pi rl\) (where \(l = \sqrt{r^{2}+h^{2}}\) for a cone with radius \(r\) and height \(h\)), and the lateral surface area of a cylinder \(S_{cylinder}=2\pi rh\).

Step2: Compare the two areas

Since \(l=\sqrt{r^{2}+h^{2}}>h\) (by the Pythagorean theorem, for non - zero \(r\) and \(h\)), then \(\pi rl>\pi rh\). And \(2\pi rh >\pi rh\). Also, \(\pi rl
eq\pi rh\) (because \(l
eq h\) when \(r> 0\)). So the lateral surface area of cone \(A\) is not \(\frac{1}{2}\) of the lateral surface area of cylinder \(B\).

Answer:

B. False