Question

4.6 surface area of prisms and cylinders
find the surface area of the cylinders. use 3.14 for π and round your answer to the nearest hundredth.
a. sa =
cm²
b. sa =
cm²

Explanation:

Step1: Recall surface - area formula for cylinder

The surface - area formula of a cylinder is $SA = 2\pi r^{2}+2\pi rh$, where $r$ is the radius of the base and $h$ is the height of the cylinder.

Step2: Solve for part a

Given $r = 2$ cm and $h = 5$ cm. First, calculate $2\pi r^{2}$:
$2\times3.14\times2^{2}=2\times3.14\times4 = 25.12$ cm².
Then calculate $2\pi rh$:
$2\times3.14\times2\times5=62.8$ cm².
Add them together: $SA=25.12 + 62.8=87.92$ cm².

Step3: Solve for part b

Given $r=\frac{10}{2}=5$ cm and $h = 12$ cm. First, calculate $2\pi r^{2}$:
$2\times3.14\times5^{2}=2\times3.14\times25 = 157$ cm².
Then calculate $2\pi rh$:
$2\times3.14\times5\times12=376.8$ cm².
Add them together: $SA = 157+376.8 = 533.8$ cm².

Answer:

a. $87.92$ cm²
b. $533.80$ cm²