Answer:
36.4 % is the surface area of the ottoman is green .
Step-by-step explanation:
Formula
\(Surface\ area\ of\ a\ cylinder = 2 \pi r h + \pi r^{2}\)
(Not included the bottom surface area)
Where r is the radius and h is the height .
As shown in the diagram.
h = 6 + 8
= 14 in
r = 16 in
Put the values in the formula
\(Surface\ area\ of\ whole\ ottoman = \pi ( 2 r h + r^{2})\)
Putting the value in the above
\(Surface\ area\ of\ whole\ ottoman = \pi ( 2\times 16\times 14 + 16\times 16)\)
\(Surface\ area\ of\ whole\ ottoman =\pi ( 448+256)\)
\(Surface\ area\ of\ whole\ ottoman = \pi (704)\ in\)
Now find out the surface area of the green ottoman .
r = 16 in
h = 8 in
Put all the values in the formula
\(Surface\ area\ of\ green\ ottoman = \pi ( 2 r h)\)
\(Surface\ area\ of\ green\ ottoman = \pi ( 2\times 8\times 16)\)
\(Surface\ area\ of\ green\ ottoman = \pi ( 256)\ in\)
Formula
\(Percentage = \frac{Surface\ area\ of\ green\ ottoman\times 100}{Total\ surface\ area\ of\ whole\ ottoman}\)
Putting the values in the above
\(Percentage = \frac{ 256 \pi\times 100}{ 704 \pi}\)
\(Percentage = \frac{25600}{704}\)
Percentage = 36.4 % (Approx)
Therefore the 36.4% is the surface area of the ottoman is green .
