The length, breadth and height of a room in a house are 8 cm, 6 cm and 4 m respectively. The house owner decides to paint the four walls of the room at the cost of Rs. 0.045 per $c{{m}^{2}}$ of wall. How much will the owner spend in painting the walls?

Question

The length, breadth and height of a room in a house are 8 cm, 6 cm and 4 m respectively. The house owner decides to paint the four walls of the room at the cost of Rs. 0.045 per $c{{m}^{2}}$ of wall. How much will the owner spend in painting the walls?

Vedantu Content Team · Accepted Answer

Hint: Assume length, breadth and height of the room be l, b and h respectively. Change the given height into centimeters. Find out the surface area that is going to be painted by applying the formula of lateral surface area of a cuboid given by $L.S.A=2h\left( l+b \right)$. Then multiply the total area obtained with the rate of painting the wall. Complete step-by-step solution -A cuboid is a $3D$ shape. Cuboids have 6 faces, 12 vertices and 8 edges. Cuboids are made from 6 rectangles which are placed at right angles. A cuboid that uses all square faces is a cube. Total surface area of a cuboid is the area of six rectangles and curved surface area is the area of 4 rectangles containing height. T.S.A of cuboid $=2\left( lb+bh+hl \right)$ and, L.S.A of cuboid $=2\times \left( l+b \right)\times h$

Now, we come to the question. As it is given that the owner is painting the four walls of the room. So, the total surface area the owner has to paint is the lateral surface area of the room. We have been provided with: l = 8 cm, b = 6 cm and h = 4 m Changing the height into cm, we get, h = 400 cm Therefore, area to be painted $\begin{align}  & =2\times \left( l+b \right)\times h \\  & =2\times \left( 8+6 \right)\times 400 \\  & =11200\text{ c}{{\text{m}}^{\text{2}}} \\ \end{align}$ Now, cost of painting four walls $\begin{align}  & =\text{total area to be painted }\times \text{ rate per unit area} \\  & \text{=112}\times 0.04\text{5} \\  & \text{=504} \\ \end{align}$ Hence, the total cost of painting is Rs. 504. Note: One may note that it is necessary to convert all the dimensions into the same unit otherwise it will be the wrong approach. We have converted the given height into cm because the other two dimensions were in cm and also the rate was given in per square cm.