Question

find the surface area in terms of pi.
#39 & #41

Answer 1

#39
top is a half cylinder
radius = 7
height = 8

Answer 2

ok so how do I do this problem (like setting it up with the formula)

Answer 3

first find the surface area of top thing

Answer 4

use surface area of cylinder formula

Answer 5

\[SA=2\pi rh+ 2\pi r^2\]
\[SA=2\pi (7*8)+ 2\pi (7)^2\]
\[SA=2 \pi 56+ 2 \pi 49\]
\[SA=2(56)\pi+ 2(49)\pi\]\[SA=112\pi+98\pi\]
\[SA=210 \pi\]

Answer 6

like that?

Answer 7

Yes, but u dont have a full cylinder there. You only have half. so talk half of it

Answer 8

after that, you need to work the bottom composite figure

Answer 9

so it is \[SA=105\pi\]

Answer 10

SA of top half cylinder = \(105 \pi\)

Answer 11

bottom figure :
radius = 4
height =8

correct?

Answer 12

im confused on how to do this part

Answer 13

No. you need to split bottom composite figure into two figures :-
1) cylinder on right side
2) prism on left side

Answer 14

look at right side, its a half cylinder with radius =7, height = 4.
stare at the figure for few seconds, and convince urself first

Answer 15

oh okay I see n0w

Answer 16

\[SA= 2\pi (7*4)+ 2 \pi (7)^2\]
\[SA=2 \pi(28)+ 2 \pi(49)\]
\[SA=2(28)\pi+2(49)\pi\]
\[SA=56\pi+98\pi\]
\[SA=154\pi\]
\[SA=154\pi*\frac{ 1 }{ 2 }=77 \pi\]

Answer 17

ok so now what

Answer 18

okay so wat other sides we need to add ?

Answer 19

the left side

Answer 20

yes, we wont be using a direct formula here.
lets calculate area of each side separately and add them up of

Answer 21

ok so how to I do the left side ?

Answer 22

Left side :-
1) bottom rectangle area = 8*14 = 112
2) are of left rectangle = 4*14 = 56
3) are of front and back rectangles = 2(8*4) = 64

add them up.

Answer 23

*area

Answer 24

232

Answer 25

ok now what

Answer 26

add all areas 232 + top half cylinder + right half cylinder

Answer 27

\[(182\pi+232)cm^2\]

Answer 28

correct !

Answer 29

so since ive finished 39, how do I do 41