Question

1. which statements are true about the surface area of the given cylinders? select all that apply.□ the cylinders have the same surface area.□ the surface area of cylinder a is greater than that of cylinder b.□ the surface area of cylinder b is greater than that of cylinder a.□ the surface area of cylinder a is half that of cylinder b.□ the surface area of cylinder b is half that of cylinder a.cylinder a: height 12 m, radius 8 mcylinder b: height 12 m, radius 8 m7-4 find surface area of cylinders 421

Explanation:

Step1: Recall cylinder surface area formula

The total surface area of a cylinder is $SA = 2\pi r^2 + 2\pi rh$, where $r$ is radius and $h$ is height.

Step2: Calculate Cylinder A's surface area

Cylinder A: $r=8$ m, $h=12$ m
$SA_A = 2\pi(8)^2 + 2\pi(8)(12) = 2\pi(64) + 2\pi(96) = 128\pi + 192\pi = 320\pi$

Step3: Calculate Cylinder B's surface area

Cylinder B: $r=12$ m, $h=8$ m
$SA_B = 2\pi(12)^2 + 2\pi(12)(8) = 2\pi(144) + 2\pi(96) = 288\pi + 192\pi = 480\pi$

Step4: Compare the two surface areas

$480\pi > 320\pi$, so $SA_B > SA_A$

Answer:

$\square$ The cylinders have the same surface area.
$\square$ The surface area of Cylinder A is greater than that of Cylinder B.
$\checkmark$ The surface area of Cylinder B is greater than that of Cylinder A.
$\square$ The surface area of Cylinder A is half that of Cylinder B.
$\square$ The surface area of Cylinder B is half that of Cylinder A.