Question

question 4 of 10
the cone and the cylinder below have equal surface area.
a. true
b. false

Explanation:

Step1: Calculate the surface area of the cone

The surface area formula of a cone \(S_{cone}=\pi r(r + l)\), where \(r\) is the radius and \(l\) is the slant height. Given \(l = 2r\), then \(S_{cone}=\pi r(r + 2r)=3\pi r^{2}\).

Step2: Calculate the surface area of the cylinder

The surface area formula of a cylinder \(S_{cylinder}=2\pi r(r + h)\). Given \(h = r\), then \(S_{cylinder}=2\pi r(r + r)=4\pi r^{2}\).

Step3: Compare the two surface areas

Since \(3\pi r^{2}
eq4\pi r^{2}\), the cone and the cylinder do not have equal surface areas.

Answer:

B. False