Question

select the correct answer. engineers are designing a cylindrical sensor for scientific equipment used in space exploration. the surface area of the sensor must be no more than 100.48 square centimeters and the sensor is 6 cm long. what is the maximum radius of the sensor? 2 cm 4 cm 1 cm 8 cm

Explanation:

Step1: Recall total surface area formula

Total surface area of a cylinder: $SA = 2\pi r^2 + 2\pi r h$

Step2: Substitute known values

$SA \leq 100.48$, $h=6$, use $\pi=3.14$:
$2(3.14)r^2 + 2(3.14)r(6) \leq 100.48$

Step3: Simplify the inequality

$6.28r^2 + 37.68r - 100.48 \leq 0$
Divide all terms by 6.28:
$r^2 + 6r - 16 \leq 0$

Step4: Solve quadratic equation

Factor: $(r+8)(r-2) \leq 0$
Solutions: $r=-8$ (discard, radius>0) or $r=2$

Answer:

2 cm