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. 1.7 m
b. 4.1 m
c. 2.0 m
d. 2.9 m

Explanation:

Step1: Calculate cylinder surface area

The total surface area of a cylinder is $SA_{cylinder}=2\pi r(r+h)$, where $r=1.5$ m, $h=4$ m.
$$SA_{cylinder}=2\pi(1.5)(1.5+4)=2\pi(1.5)(5.5)=16.5\pi$$

Step2: Set sphere surface area equal

Sphere surface area: $SA_{sphere}=4\pi R^2$. Set equal to cylinder SA:
$$4\pi R^2=16.5\pi$$

Step3: Solve for sphere radius R

Cancel $\pi$, rearrange to solve for $R$:
$$R^2=\frac{16.5}{4}=4.125$$
$$R=\sqrt{4.125}\approx2.0$$

Answer:

C. 2.0 m