Question

select the correct answer.
a cylinder has a height of 4 meters and a radius of 1.5 meters. what is the approximate radius of a sphere that has the same surface area as the cylinder?
a. 2.0 m
b. 4.1 m
c. 1.7 m
d. 2.9 m

Explanation:

Step1: Calculate the surface area of the cylinder

The formula for the surface area of a cylinder \(S = 2\pi r(r + h)\). Given \(r = 1.5\space m\) and \(h=4\space m\), substitute into the formula:

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Step2: Calculate the radius of the sphere

The formula for the surface area of a sphere \(S = 4\pi R^{2}\). Since the surface area of the sphere is equal to the surface area of the cylinder, we have \(4\pi R^{2}=16.5\pi\). Divide both sides by \(\pi\): \(4R^{2}=16.5\). Then \(R^{2}=\frac{16.5}{4}=4.125\). Take the square root: \(R=\sqrt{4.125}\approx2.0\space m\)

Answer:

A. 2.0 m