Question

The dimensions of a room are 12.5 m by 9 m by 7 m. There are 2 doors and 4 windows in the room; each door measures 2.5 m by 1.2 m and each window 1.5 m by 1 m. Find the cost of painting the walls at Rs 3.50 per square metre.

Answer 1

\[\text { The dimensions of the room are 12 . 5 m } \times 9 m \times 7 m . \]

\[\text { Hence, the surface area of walls = 2 } \times \text { (length } \times\text {  height + breadth  }\times \text { height) }\]

\[ = 2 \times (12 . 5 \times 7 + 9 \times 7)\]

\[ = 301 m^2 \]

\[\text { Also, there are 2 doors and 4 windows in the room  } \]

\[\text { The dimensions of door are 2 . 5 m } \times 1 . 2 m . \]

\[\text { i . e . , area of a door } = 2 . 5 \times 1 . 2 = 3 m^2 \]

\[ \therefore \text { Total area of 2 doors = 2 } \times 3 = 6 m^2 \]

\[\text { The dimensions of a window are 1 . 5 m } \times 1 m . \]

\[\text { i . e . , area of a window = 1 . 5  }\times 1 = 1 . 5 m^2 \]

\[ \therefore \text { Total area of 4 windows = 4  }\times 1 . 5 = 6 m^2 \]

\[\text { Hence, the total area to be painted = 301 - (6 + 6) = 289 } m^2 \]

\[\text { The rate of painting 1 }m^2 \text { of wall = Rs 3 . 50 }\]

\[ \therefore \text { The total cost of painting 289 } m^2 \text { of wall = Rs 289 } \times 3 . 50 = Rs 1011 . 50\]