The length, the breadth and the height of a closed cuboidal box are 2.5 m , 2 m and 90 cm, respectively. What would be the cost of a concave needed to cover this box completely, if the cost of the canvas is ₹70 per $$m^2$$ ?​

Correct option is B

Given:

Dimensions of the closed cuboidal box:

Length (L) = 2.5 m

Breadth (B) = 2 m

Height (H) = 90 cm = 0.9 m

Cost of canvas per square meter = ₹70/m².

The total cost of canvas to cover the box completely.

Solution:

Surface Area of the Cuboidal Box

The surface area of a closed cuboidal box is given by:

Surface Area = 2 × [L × B + B × H + H × L]

Substitute the given values:

L = 2.5 m, B = 2 m, H = 0.9 m

Surface Area = 2 × [(2.5 × 2) + (2 × 0.9) + (0.9 × 2.5)]

Calculate each term:

2.5 × 2 = 5

2 × 0.9 = 1.8

0.9 × 2.5 = 2.25

Now, sum up:

5 + 1.8 + 2.25 = 9.05

Multiply by 2:

Surface Area = 2 × 9.05 = 18.1 m²

Step 3: Calculate the Cost of Canvas

Cost = Surface Area × Cost per m²

Cost = 18.1 × 70

Multiply:

Cost = ₹1267

The total cost of the canvas to cover the box completely is ₹1267.