A cuboid has the totol surface area 432 cm2 . if its length and breath are 12 cm and 6cm respectively . what is height ?
Answers
Answer:
THE HIGHT OF THE CUBE IS 6 CM
Step-by-step explanation:
12*6 = 72CM
THEN DIVIDE 432 BY 72
YOU WILL GET 6
Answer :
• Height of the cuboid = 8 cm
Given :
- Total surface area of cuboid = 432 cm²
- Length of the cuboid = 12 cm
- Breadth of the cuboid = 6 cm
To find :
- Height of the cuboid
Knowledge Required :
Formula of total surface area of cuboid :-
⠀⠀⠀⇒ Total surface area of cuboid = 2(lb + bh + hl)
where,
• l denotes the length of the cuboid
• b denotes the breadth of the cuboid
• h denotes the height of the cuboid
Solution :
Substitute the given values in the formula of total surface area of cuboid to find the value of height of the cuboid :
⠀⠀⠀⇒ TSA = 2(lb + bh + hl)
⠀⠀⠀⇒ 432 = 2(12 × 6 + 6 × h + h × 12)
⠀⠀⠀⇒ 432 = 2(72 + 6h + 12h)
⠀⠀⠀⇒ Transposing 2 to the left hand side :
⠀⠀⠀⇒ 432 ÷ 2 = 72 + 6h + 12h
⠀⠀⠀⇒ 216 = 72 + 6h + 12h
⠀⠀⠀⇒ 216 = 72 + 18h
⠀⠀⠀⇒ Transposing 72 to the other side and changing its sign from positive into negative :
⠀⠀⠀⇒ 216 - 72 = 18h
⠀⠀⠀⇒ 144 = 18h
⠀⠀⠀⇒ Transposing 8 to the left hand side :
⠀⠀⠀⇒ 144/18 = h
⠀⠀⠀⇒ Dividing the numbers by 2, we get :
⠀⠀⠀⇒ 72/9 = h
⠀⠀⠀⇒ Dividing the numbers by 3, we get :
⠀⠀⠀⇒ 24/3 = h
⠀⠀⠀⇒ Dividing the numbers by 3, we get :
⠀⠀⠀⇒ 8 = h
The value of h = 8
Therefore, the height of the cuboid = 8 cm
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VERIFICATION :
To verify the value of height of the cuboid, calculate the total surface area of cuboid if it will be equal to 432 cm² (as mentioned in the question) then the value of height is right.
⠀⠀⠀⇒ TSA of cuboid = 2(lb + bh + hl)
we have,
- l = 12 cm, b = 6 cm and h = 8 cm
⠀⠀⠀⇒ TSA of cuboid = 2(12 × 6 + 6 × 8 + 8 × 12)
⠀⠀⠀⇒ TSA of cuboid = 2(72 + 48 + 96)
⠀⠀⠀⇒ TSA of cuboid = 2(216)
⠀⠀⠀⇒ TSA of cuboid = 432
The total surface area of cuboid = 432 cm²
Hence, verified.