Question

question 5 (1 point)
the surface area, in square centimeters, of the right cylinder below is ____.

image of a right cylinder with radius 7 cm and height 12 cm

options:

• ((7^2)pi + 14pi(12) = 217pi)
• (14pi(12) = 168pi)
• (98pi + (14pi)(12) = 266pi)
• ((7^2)(12) = 588pi)

Explanation:

Step1: Recall cylinder surface area formula

The total surface area of a right cylinder is the sum of the areas of the two circular bases and the lateral (curved) surface area: $SA = 2\pi r^2 + 2\pi r h$

Step2: Identify given values

Radius $r = 7$ cm, height $h = 12$ cm

Step3: Calculate base areas

$2\pi r^2 = 2\pi (7)^2 = 2\pi(49) = 98\pi$

Step4: Calculate lateral surface area

$2\pi r h = 2\pi(7)(12) = 168\pi$

Step5: Sum the two areas

$SA = 98\pi + 168\pi = 266\pi$

Answer:

$98p + 14p(12) = 266p$