Question

What percent of the surface area of the ottoman is green (not including the bottom)? Round to the nearest tenth.

Answer 1

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 .

Answer 2

Total Area = r² π + 2 r h π = 6² π + 2 * 6 * 14 π = 204 π in²
Green Area = 2 * 6 * 8 π = 96 π in²
204 π ---------------100 %
96 π ----------------- x %
---------------------------------
x = ( 96 * 100 ) / 204 = 47.0588 ≈ 47.1
Answer:
About 47.1 % of the ottoman is green ( not including the bottom ).