Final answer:
To paint the room, Daniel will need to paint a total area of 500 m². Since each can covers 100 m², he will need 5 cans of paint.
Step-by-step explanation:
The student is asking how many cans of paint Daniel will need to paint the walls and ceiling of a cuboidal hall with dimensions given as a length of 15 m, breadth of 10 m, and height of 7 m. It is also specified that each can of paint covers 100 m².
To find the total paintable surface area, we must calculate the areas of all the walls and the ceiling. The walls consist of two sets of opposite walls, with each pair having the same dimensions. Therefore, we calculate two pairs of rectangular areas:
- Two walls of area 15 m (length) × 7 m (height) = 105 m² each.
- Two walls of area 10 m (breadth) × 7 m (height) = 70 m² each.
Adding the areas of these walls:
2 × 105 m² + 2 × 70 m² = 210 m² + 140 m² = 350 m².
Now we calculate the area of the ceiling, which is simply the product of the length and breadth:
15 m (length) × 10 m (breadth) = 150 m².
The total area to be painted is therefore:
350 m² (walls) + 150 m² (ceiling) = 500 m².
To find out how many cans of paint are needed, we divide the total area by the area coverage of one can:
500 m² ÷ 100 m² = 5 cans.
Daniel will need 5 cans of paint to paint the whole room.