Answer:
Exact surface area = 500+20pi square cm
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Explanation:
- A = area of the bottom face = 10*12 = 120
- B = area of the left face = 7*12 = 84
- C = area of the right face = 7*12 = 84
- D = area of the front face = 7*10-0.5*pi*2^2 = 70 - 2pi
- E = area of the back face = 7*10-0.5*pi*2^2 = 70 - 2pi
- F = area of the top face = 2*3*12+0.5*2*pi*2*12 = 72+24pi
All areas mentioned are in square cm, which can be abbreviated to cm^2.
Faces A,B,C are straight forward as they are simply rectangles. The remaining 3 other faces are a bit tricky.
Faces D and E involve subtracting off the area of a semicircle of radius 2 from a 7 by 10 rectangle area. The formula pi*r^2 is the area of a full circle, while 0.5*pi*r^2 is the area of a semicircle. From there, I then plugged in r = 2.
The top face is really a combination of 3 different pieces (two flat, one curved in the middle). Each flat part is of area 3*12 = 36, so that doubles to 2*3*12 when accounting for both flat parts. The curved portion will involve the lateral surface area of a cylinder formula which is
LSA = 2*pi*r*h
but since we're only dealing with half the lateral area, we multiply that by 0.5 to get 0.5*2*pi*r*h. From there, I plugged in r = 2 and h = 12.
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In summary we have these six areas for the faces
- bottom = 120
- left = 84
- right = 84
- front = 70 - 2pi
- back = 70 - 2pi
- top = 72 + 24pi
Add up those sub areas to get the full surface area of this particular 3D solid.
120+84+84+(70-2pi)+(70-2pi)+(72+24pi)
(120+84+84+70+70+72)+(-2pi-2pi+24pi)
500+20pi
This is the exact surface area in terms of pi. If you want the approximate version of this, then you could replace pi with 3.14 and compute to get 562.8 cm^2
Use more decimal digits in pi to get a more accurate value. If you use your calculators version of pi, then you should get somewhere around 562.831853 cm^2
In this case, I think it's better to stick with the exact surface area (unless your teacher instructs otherwise).
