Answer:
Total surface area=
304+9pi
~= 332.3
Step-by-step explanation:
Surface area is the areas of all the parts/sides/surfaces of the shape all added together.
There is a BOTTOM, 4 SIDES, a flat TOP, and a DOME shape.
The BOTTOM and SIDES are rectangles, so you can get the areas by multiplying length × width (or b•h)
BOTTOM: 8×10 =80
SIDES: There are 4×8 sides. 4×8 = 32. There are two of them 2×32=64.
There are 4×10 sides. 4×10 = 40. There are two of them, 2×40 = 80
For the flat TOP, it is also 8×10=80, but it has a circle cut out of it. Or, well, the circle that's under the dome doesn't count bc of the dome. So we'll take it away.
CIRCLE (under the dome):
Area of a circle is A=pi•r^2= pi•3^2
A = 9pi
So the flat TOP is:
80 - 9pi ~= 51.7
The DOME is a hemisphere (a half ball shape). Surface Area of a sphere is 4pi•r^2 We find that, then take half.
DOME =
4pi•3^2•(1/2)
= 4pi•9•(1/2)
= 18pi
~= 56.5
Now add up all the pieces:
80+64+80+80-9pi+18pi
= 304+9pi
~= 304 +28.3
= 332.3
