Question

The cost of paint is Rs. 60 per kilogram. A kilogram of paint covers $20d{{m}^{2}}$ . How much will it cost to paint the outside of a cube having each side of 10dm?
(a) Rs. 3000
(b) Rs. 900
(c) Rs. 1800
(d) Rs. 360

Answer 1

Hint: Start by finding the total area that needs to be painted, i.e., the total surface area of the cube using the formula $6{{a}^{2}}$ , where a is the side length of cube. Once you get the total surface area, divide it by the area that can be painted with 1 kilogram of paint and multiply the result by the cost of each kilogram of paint to get the total cost of painting.

Complete step-by-step answer:
It is given that we need to paint a cube completely whose sides are 10dm. So, we have to paint the whole surface area of the cube and we know that the total surface area of the cube is given by the formula $6{{a}^{2}}$ , where a is the side length of the cube.

$\therefore \text{Total surface area to be painted}=6{{a}^{2}}=6\times {{10}^{2}}=600d{{m}^{2}}$
Now let us find the amount of paint required. It is given that 1 kilogram of paint is sufficient to paint 20 sq dm of area. So, the amount of paint required to paint 600 sq dm of area is:
$\text{Amount of paint required}=\dfrac{\text{Total Area}}{\text{Area that can be painted per kilogram}}=\dfrac{600}{20}=30kg$
Now to find the total cost of the paint we will multiply the amount by cost of 1 kg of paint. It is given in the question as Rs. 60 per kilogram.
$\therefore \text{Total cost}=30\times 60=Rs.1800$
Hence, we can conclude that the answer is option (c).

Note: Don’t be in a hurry and miss the step of dividing the total surface area by the area that can be painted by 1kg of the paint, as in the question the cost given in the question is not the cost of painting 1sq unit of area but it’s the cost of 1 kg of paint. Also, be careful about the units of the measurement that you are using.