A cube of a metal of 17 cm is melted and casted into cuboid whose base is 10.5 x 3.4 .
Find the height and surface area of the cuboid.
Answers
Answer :
- Height of the cuboid = 137.62 cm
- Surface area of cuboid = 3,897.236 cm²
Given :-
- Side of the cube = 17 cm
- The same cube with side 17 cm melted and casted into a cuboid.
- Length of the cuboid = 10.5 cm
- Breadth of the cuboid = 3.4 cm
To find :-
- Height of the cuboid
- Surface area of the cuboid
Knowledge Required :-
→ Formula of volume of cube :-
- Volume of cube = side³
→ Formula of volume of cuboid :-
- Volume of cuboid = l × b × h
→ Formula of surface area of cuboid :-
- Surface area of cuboid = 2(lb + bh + hl)
where,
- l = length of the cuboid
- b = breadth of the cuboid
- h = height of the cuboid
Understanding the question :-
As we know,
- Volume always remains same even when a substance is melted and then casted into a different shape.
So, firstly we will find the volume of the cube. The volume of the cube will be equal to volume of cuboid. From there we will find the height of cuboid.
And then by using the formula of surface area of cuboid, we will find its value.
Solution :-
Volume of cube :-
⠀⠀⠀⇒ Volume = side³
⠀⠀⠀⇒ Volume = (17)³
⠀⠀⠀⇒ Volume = 4913
Volume of cube = 4913 cm³
Volume of cube = Volume of cuboid
∴ Volume of cuboid = 4913 cm³
⠀⠀⠀⇒ Volume of cuboid = l × b × h
⠀⠀⠀⇒ 4913 = 10.5 × 3.4 × h
⠀⠀⠀⇒ 4913 = 35.7 × h
⠀⠀⠀⇒ 4913/35.7 = h
⠀⠀⠀⇒ 137.62 = h
Height of the cuboid = 137.62 cm
Surface area of cuboid :-
⠀⠀⠀⇒ Surface area = 2(lb + bh + hl)
⠀⠀⠀⇒ Surface area = 2(10.5 × 3.4 + 3.4 × 137.62 + 137.62 × 10.5)
⠀⠀⠀⇒ Surface area = 2(35.7 + 467.908 + 1,445.01)
⠀⠀⠀⇒ Surface area = 2 × 1,948.618
⠀⠀⠀⇒ Surface area = 3,897.236
Surface area of cuboid = 3,897.236 cm²