Question

the formula for the surface area of a cylinder is $2\pi r(r + h)$ where $r$ is the radius of the cylinder’s base and $h$ is its height. a certain pole has a cylinder - like shape, where the base’s radius is 10 centimeters and the height is 2 meters. what calculation will give us the estimated surface area of the pole in square centimeters? choose 1 answer. a $2\pi \cdot 10 \cdot 12$ b $2\pi \cdot 10 \cdot 210$ c $2\pi \cdot 0.01 \cdot 2.01$ d $2\pi \cdot 0.01 \cdot 200.01$

Explanation:

Step1: Convert height to cm

Height \( h = 2 \) meters \( = 2\times100 = 200 \) cm? Wait, no, wait. Wait, the radius is 10 cm? Wait, no, the problem says "the base’s radius is 10 centimeters and the height is 2 meters". So first, convert height to centimeters: \( 2 \) meters \( = 2\times100 = 200 \) cm? Wait, no, wait, the formula is \( 2\pi r(r + h) \). Wait, \( r = 10 \) cm, \( h = 2 \) meters \( = 200 \) cm? Wait, no, maybe I misread. Wait, the options: let's check the options. Option B is \( 2\pi \cdot 10 \cdot 210 \), option A is \( 2\pi \cdot 10 \cdot 12 \), option C is \( 2\pi \cdot 0.01 \cdot 2.01 \), option D is \( 2\pi \cdot 0.01 \cdot 200.01 \). Wait, maybe the height is 2 meters, but we need to convert radius to meters? Wait, no, the surface area is in square centimeters. So radius \( r = 10 \) cm, height \( h = 2 \) meters \( = 200 \) cm. Then \( r + h = 10 + 200 = 210 \) cm. Then the formula is \( 2\pi r(r + h) = 2\pi \times 10 \times 210 \). So that's option B.

Step2: Verify units and formula

The formula for the surface area of a cylinder is \( 2\pi r(r + h) \). Here, \( r = 10 \) cm (radius), \( h = 2 \) meters \( = 200 \) cm (height). So \( r + h = 10 + 200 = 210 \) cm. Substituting into the formula: \( 2\pi \times 10 \times 210 \), which matches option B.

Answer:

B. \( 2\pi \cdot 10 \cdot 210 \)