Question

1. determine the surface area of the following 3 - d objects. round to the nearest whole number and include units.

a. we know

b. we know

Explanation:

Step1: Recall cylinder surface - area formula

The surface - area formula of a cylinder is $SA = 2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height. Given $r = 4$ m and $h = 14$ m.
$SA=2\pi(4)^2+2\pi(4)(14)$

Step2: Calculate each term

First term: $2\pi(4)^2=2\pi\times16 = 32\pi$
Second term: $2\pi(4)(14)=112\pi$
Then $SA=32\pi + 112\pi=144\pi$

Step3: Evaluate and round

$SA\approx144\times3.14159 = 452.389$
Rounding to the nearest whole number, $SA\approx452$ m²

Step4: Recall cone surface - area formula

The surface - area formula of a cone is $SA=\pi r^2+\pi rl$, where $r$ is the radius, $l$ is the slant height. Given $r = 50$ mm and $l = 65$ mm.
$SA=\pi(50)^2+\pi(50)(65)$

Step5: Calculate each term

First term: $\pi(50)^2 = 2500\pi$
Second term: $\pi(50)(65)=3250\pi$
Then $SA=2500\pi+3250\pi = 5750\pi$

Step6: Evaluate and round

$SA\approx5750\times3.14159=18064.1425$
Rounding to the nearest whole number, $SA\approx18064$ mm²

Answer:

The surface area of the cylinder is approximately 452 m².
The surface area of the cone is approximately 18064 mm².