Question

18 donna paints ornaments for a school play. each ornament is made up of two identical cylinders, as shown. all surfaces of each cylinder must be painted. how many cans of paint does she need to paint 70 ornaments?
one can of paint covers 2,000 cm².
4.1 cm
6.2 cm

Explanation:

Step1: Find 1 cylinder's surface area

Surface area of a cylinder: $SA = 2\pi r^2 + 2\pi rh$
Here, $r = 4.1$ cm, $h = 6.2$ cm
$SA_1 = 2\pi(4.1)^2 + 2\pi(4.1)(6.2)$
$SA_1 = 2\pi(16.81) + 2\pi(25.42)$
$SA_1 = 33.62\pi + 50.84\pi = 84.46\pi \approx 84.46\times3.1416 \approx 265.3$ cm²

Step2: Find 1 ornament's surface area

1 ornament = 2 cylinders, so:
$SA_{ornament} = 2\times265.3 = 530.6$ cm²

Step3: Find total area for 70 ornaments

$Total_{SA} = 70\times530.6 = 37142$ cm²

Step4: Calculate number of paint cans

Each can covers 2000 cm²:
$Number_{cans} = \frac{37142}{2000} = 18.571$
Since partial cans are not sold, round up to the next whole number.

Answer:

19 cans of paint