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 surface - area formula for cylinder

The surface - area formula of a cylinder is $S = 2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height. Given $r = 4$ m and $h=14$ m.
$S_1=2\pi\times4^2 + 2\pi\times4\times14$
$=2\pi\times16+2\pi\times56$
$=32\pi + 112\pi$
$=144\pi$ m$^2\approx452$ m$^2$ (rounded to the nearest whole number)

Step2: Recall surface - area formula for cone

The surface - area formula of a cone is $S=\pi r(r + l)$, where $r$ is the radius and $l$ is the slant height. Given $r = 25$ mm (since $d = 50$ mm, $r=\frac{d}{2}=25$ mm) and $l = 65$ mm.
$S_2=\pi\times25\times(25 + 65)$
$=\pi\times25\times90$
$=2250\pi$ mm$^2\approx7069$ mm$^2$ (rounded to the nearest whole number)

Answer:

a. The surface area of the cylinder is approximately $452$ m$^2$.
b. The surface area of the cone is approximately $7069$ mm$^2$.