A cuboid has a total surface area of 100 m² and the lateral surface area is 50 m². Find the area of
its base
Answers
Given TSA of cuboid=100m
2
TSA of cuboid =50m
2
we know TSA =2[lb+bh+lh]
& CSA = 2[bh + lh]
Then TSA - CSA = 2[lb + bh + lh] -2 [bh + lh]
100 - 50 = 2lb
[lb=25m
2
]
∴ area of base is 25m
2
solution
★ Given:
TSA of cuboid = 100 m²
LSA of cuboid = 50 m²
★ To Find:
The area of its base.
★ Solution:
TSA formula of a cuboid = 2 (lh + bh + lb)
LSA formula of a cuboid = 2 (lh + bh)
We have to find the area of the base.
When we subtract the LSA from the TSA, the equation formed is as follows:
2 (lh + bh + lb) - 2 (lh + bh)
= 2lh + 2bh + 2lb - 2lh - 2bh
[Cancelling out the negative and positive values]
= 2lb ---------- (1)
Now, instead of the variables, we can put the values in the formula:
= 100 - 50
= 50 ---------- (2)
So, combining equations (1) and (2):
2lb = 50
lb = 50/2 = 25 m²
Hence the area of the base of the cuboid is 25 m².
Important Formulae related to Cuboids:
→ TSA = 2 (lh + bh + lb)
→ LSA = 2 (lh + bh)
→ Volume = lbh