Question

Observe the composite figure below.



The bottom shape is a cube with base edges of 16 meters. The top shape is a right pyramid with a height of 15 meters. What is the surface area of this composite figure?
Answer
544 m2
1,280 m2
1,824 m2
2,080 m2

Answer 1

What's your working so far? How are you approaching this?

Answer 2

i have made it absolutely no where on this problem.

Answer 3

Do you know what the area of a square is?

Answer 4

yesss

Answer 5

Great! So try to divide the figure into two parts:

1. the pyramid
2. The cube

Answer 6

Now, a cube's surface is basically 6 squares, so what would the area of the surface of the cube be?

Answer 7

256???

Answer 8

That's the area of one square. A cube's surface is made of 6 squares. So the surface area of the cube is 6 times the area of a square, right?

Answer 9

so that would be 1,536

Answer 10

Yeah, so that's the surface area of the bottom part.

Now let us look at the top part, it is a right pyramid, which is basically 4 triangles and a square on the surface

Answer 11

DO you have the formula for the surface area of a right pyramid?

Answer 12

B+ 1/2ps?

Answer 13

yes

Answer 14

Exactly, for the pyramid your main problem is finding s
what's the formula for s?

You're very close!

Answer 15

i have no idea ! haha

Answer 16

B is the area of the base, which is a square, which you calculated above was 256! P is the perimeter of the base, which is the sum of all sides of the base,
So P = 16 + 16 + 16 + 16 = 64

Answer 17

So we are left with s, which is the slant height. Slant height
\[s=\sqrt{{h^2}+{r^2}}\]

where h is the height, and r is the radius of the base

The radius of the base is half the side of the square, so r = 8.

Can you calculate s?

Answer 18

289?

Answer 19

17

Answer 20

nno 288

Answer 21

16

Answer 22

No no, square root that! You are on the right track tahtah99 :)

Answer 23

yess, 17!

Answer 24

So, you said the formula was
B + 1/2Ps

B = 256 (area of square)
P = 64 (perimeter of square)
s = 17

So total surface area of the pyramid is?

Answer 25

800 ?

Answer 26

Great! That's correct.

Answer 27

see i told you!!

Answer 28

you got it!!

Answer 29

-_____- hahah

Answer 30

So now, you have a pyramid and a cube
Area of pyramid = 800
Area of cube = 1536

Now if you join the two, you will not see one side of the cube, and the base of the pyramid. Do you understand that?

Answer 31

It's not done yet :D

Answer 32

dont celebrate, its not done yet!!

Answer 33

oh Lord..
yeah i understand

Answer 34

So you have to subtract the area of two things:
1. The base of the pyramid
2. One square from the cube.

Answer 35

so subtract 512?

Answer 36

So your final area will be:

1536 + 800 - (area of 1 square) - (area of 1 square)

= 1536 + 800 - 256 - 256

Answer 37

Exactly! You got this!

Answer 38

exactly!! WHAT I SAY?? YOU GOT IT!

Answer 39

is the answer c?

Answer 40

THATS WHAT IVE BEEN TRYING TO SAY!! YES IT IS!!!!!!

Answer 41

Yes it is!

Answer 42

Congrats :)

Answer 43

thank you so much ! : )

Answer 44

SEE! NOOOOOWWW YOU CELEBRATE!!

Answer 45

YOUR VERY WELCOME~!

Answer 46

hahahahahahha

Answer 47

Glad to help!

Answer 48

glad to help too!

Answer 49

could you check my answer for the last question ?

Answer 50

nvm got it

Answer 51

ok.