Final answer:
The length of the cuboid formed by melting a cube with a total surface area of 150 cm², with a given breadth of 5 cm and height of 4 cm, is 6.25 cm.
Step-by-step explanation:
The student is asking about the dimensions of a cuboid constructed from melting a cubical piece of silver.
The total surface area of the cube is given as 150 cm².
To find the length of the cuboid, we must first determine the volume of the silver cube, as the volume will remain constant during melting and reformation into the cuboid shape.
The surface area of the cube (SA) is calculated using the formula SA = 6s², where s is the length of one side of the cube. So, 150 = 6s² implies s² = 25, therefore s = 5 cm.
The volume (V) of the cube is V = s³, which gives us V = 5³ = 125 cm³.
Now, knowing the volume of the cuboid will be the same as the cube, we can find the length (L) using the formula for the volume of the cuboid V = L × breadth × height.
With a breadth of 5 cm and height of 4 cm, the volume equation becomes 125 = L × 5 × 4.
Solving for L gives us L = 125 /(5 × 4) = 6.25 cm. Hence, the length of the cuboid is 6.25 cm.