Surface area of a composite object.

Question

A cone with a slant height of 8.9cm and a radius of 4cm. The cones base is attached on top of a rectangular prism whose length is 41cm, width is 20cm and height is 40cm. It is attached with a hemisphere whose radius is 4cm.
Find the surface area of this composite object.

Answer 1

surely you have the formulas for finding the volumes of these solids. Just add 'em up.

What do you get? Show work if you get stuck.

Answer 2

Rectangular prism:
Sa= 2lw+2wh+2lh
2 (41)(20)+ 2 (20)(40)+ 2(41)(40)
1640+1600+3280
SA= 6520cm2
There's no overlaps for rectangular prism so it stays the same.

Cone:
SA= πrs+πr^2
π4×8.94427191+π4^2
112.3970357+50.26548246= 162.6625182cm2

Hemisphere:
SA= 3πr^2
3π4^2
SA= 150.7964474cm2

Answer 3

Now I have to find the overlap. So:
Cone πr2= 50.26548246
And I don't get how to subtract the overlap of tye hemisphere

Answer 4

And since the circle of the cone is placed on top of the cylinder, do I do 2πr^2 since it covers 2 surfaces?
Also for the hemisphere, I'm not understanding what formula to use since it is at the bottom of the rectabgular prism. They're connected.do I still use 3πr^2?

Answer 5

My total surface area I found is 6833.458965cm2
But I need to subtract the overlapping or hidden sides. I need help on that

Answer 6

Oops - my bad. I was looking for volumes.

The overlap is the area of the circular base of the cone (pi r^2) and the circular base of the hemisphere (pi r^2).

Subtract it twice, once for each solid.