Question

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

About ___ %

Answer 1

36.4 % is the surface area of the ottoman is green .

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* 16* 14 + 16* 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* 8* 16)`

`Surface\ area\ of\ green\ ottoman = \pi ( 256)\ in`

Formula

`Percentage = (Surface\ area\ of\ green\ ottoman* 100)/(Total\ surface\ area\ of\ whole\ ottoman)`

Putting the values in the above

`Percentage = ( 256 \pi* 100)/( 704 \pi)`

`Percentage = (25600)/(704)`

Percentage = 36.4 % (Approx)

Therefore the 36.4% is the surface area of the ottoman is green .