find height and LSA
cuboid= length 5 metre breath 10 metre total surface area 700
Answers
QUESTION :-
Find height and LSA cuboid whose length 5 m, breath 10 m. and total surface area 700 m²
SOLUTION :-
★ Given that,
- Total Surface Area of Cuboid = 700 m³
- Length of Cuboid(l) = 5 m.
- Breadth of Cuboid(b) = 10 m.
★ To find,
- Height of Cuboid. (h)
- LSA of Cuboid.
★ Let,
Formula for TSA of Cuboid = 2[lb + bh + lh] = 700
➠ 2[ (5 × 10) + (10 × h) + (5 × h) = 700
➠ 50 + 10h + 5h = 700/2
➠ 50 + 15h = 350
➠ 15h = 350 - 50
➠ 15h = 300
➠ h = 300/15
➠ h = 20
∴ Hence, Height of Cuboid = 20 m.
★ Verification,
- Substitute value of h in the formula to get TSA = 700 m².
➡ 2[ (5 × 10) + (10 × 20) + (5 × 20) ]
➡ 2[ 50 + 200 + 100 ]
➡ 2[ 350 ]
➡ 700
Since, LHS = RHS. Hence, it was verified.
★ Now,
We can find out LSA of Cuboid.
LSA of Cuboid = 2h(l + b)
➠ 2 × 20(5 + 10)
➠ 40(15)
➠ 600
∴ Hence, LSA of Cuboid = 600 m².
★ More Information,
◼ TSA of Cuboid = 2[ lh + bh + lh ]
◼ LSA of Cuboid = 2h(l + b)
◼ Volume of Cuboid = lbh
___________________________
⭐ QUESTION ⭐
Find the height and LSA Of A Cuboid if,
Length = 5m,
Breadth = 10m,
TSA = 700m².
⭐ SOLUTION ⭐
⚘Given⚘
- Length = 5m.
- Breadth = 10m.
- TSA = 700m²
⚘To Find⚘
- Height Of Cuboid.
- LSA Of Cuboid.
⚘Solution⚘
Formula For TSA :- 2(lb + bh + hl)
So,
➳ 2(lb + bh + hl) = 700m²
➳ 2(5 × 10 + 10 × h + 5 × h) = 700m²
➳ 2(50 + 15h) = 700m²
➳ 100 + 30h = 700m²
➳ 30h = 700 - 100
➳ 30h = 600m²
➳ h = 600/30
➳ h = 20m.
Hence, Height Of Cuboid = 20m.
Now, Calculating LSA.
Formula Of LSA :- 2(l+b)h
Put the values.
➳ 2(5+10) × 20.
➳ 2 × 15 × 20.
➳ 30 × 20.
➳ 600.
Hence, Lateral Surface Area = 600m².