A cuboid with dimensions 20cm×12cm×10cm is cut into 8 identical pieces by 3 cuts. What will be the total surface area of all the pieces?
- A1680cm
2 - B3360cm
2 - C2240cm
2 - D1220cm
2
Solution & Step-by-step Explanation
The dimensions of the original cuboid are l=20cm, b=12cm, and h=10cm.
To cut a cuboid into 8 identical pieces with 3 cuts, one cut must be made parallel to each of the three pairs of faces (one perpendicular to length, one to breadth, and one to height).
Each cut parallel to a face creates two new surfaces identical in area to that face.
A cut perpendicular to the length creates 2 new surfaces of area b×h.
A cut perpendicular to the breadth creates 2 new surfaces of area l×h.
A cut perpendicular to the height creates 2 new surfaces of area l×b.
Thus, the total surface area of the 8 pieces is equal to the original surface area plus the area of the newly created surfaces:
Total Surface Area=Original Surface Area+2(b×h)+2(l×h)+2(l×b)
Total Surface Area=2(lb+bh+lh)+2(bh+lh+lb)=4(lb+bh+lh)
Let's compute the value:
lb=20×12=240
bh=12×10=120
lh=20×10=200
Sum=240+120+200=560cm
2
Total Surface Area=4×560=2240cm
2
To cut a cuboid into 8 identical pieces with 3 cuts, one cut must be made parallel to each of the three pairs of faces (one perpendicular to length, one to breadth, and one to height).
Each cut parallel to a face creates two new surfaces identical in area to that face.
A cut perpendicular to the length creates 2 new surfaces of area b×h.
A cut perpendicular to the breadth creates 2 new surfaces of area l×h.
A cut perpendicular to the height creates 2 new surfaces of area l×b.
Thus, the total surface area of the 8 pieces is equal to the original surface area plus the area of the newly created surfaces:
Total Surface Area=Original Surface Area+2(b×h)+2(l×h)+2(l×b)
Total Surface Area=2(lb+bh+lh)+2(bh+lh+lb)=4(lb+bh+lh)
Let's compute the value:
lb=20×12=240
bh=12×10=120
lh=20×10=200
Sum=240+120+200=560cm
2
Total Surface Area=4×560=2240cm
2