Question

the formula for the surface area of a cylinder is $2\pi r(r + h)$ where $r$ is the radius of the cylinders base and $h$ is its height.
a certain pole has a cylinder - like shape, where the bases 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 centimeters

The height is 2 meters. Since 1 meter = 100 centimeters, 2 meters = \(2\times100 = 200\) centimeters. But in the formula \(2\pi r(r + h)\), we have \(r + h\). Here, \(r = 10\) cm and \(h = 200\) cm, so \(r + h=10 + 200 = 210\) cm.

Step2: Substitute into the formula

The formula for the surface area of a cylinder is \(2\pi r(r + h)\). Substituting \(r = 10\) and \(r + h = 210\), we get \(2\pi\times10\times210\).

Answer:

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