Question

The dimensions of a cuboid are in the ratio of 3:2:2 and the lateral surface area of the cuboid is 2000m square the outer surface area of the cuboid is painted with the coloured enamel @ rupees 8 per metre square find the total cost of painting the outer surface of the cuboid

Answer 1

SOLUTION:-

Given:

•The dimensions of a Cuboid are in the ratio of 3:2:2 & the lateral surface area of the cuboid is 2000m².

•The outer surface area of the Cuboid is painted with the coloured enamel Rs.8 /m².

To find:

The total cost of painting the outer surface area of the cuboid.

Explanation:

Let the length of the cuboid, L= 3R m.

Let the breadth of the cuboid,B=2R m.

Let the length of the height, H= 2R m.

We have,

Lateral surface area of the cuboid=2000m².

We know that, area of the formula of 4 walls: 2(L+ B)H

According to the question:

=) 2[3R + 2R] × 2R = 2000

=) 2[5R] × 2R= 2000

=) 10R × 2R = 2000

=) 20R² = 2000

=) R² = 2000/20

=) R² = 100

=) R= √100

=) R= 10

Now,

Formula of the outer surface area of cuboid:

=) 2(LB+BH+LH)

• Length= 3R = 3×10 = 30m
• Breadth= 2R= 2×10= 20m
• Height= 2R= 2×10= 20m

Therefore,

=) 2[30×20 + 20×20 + 30×20]m²

=) 2[600 + 400 + 600]m²

=) 2[1600]m²

=) 3200m²

Now,

Cost of painting 1m² of outer surface area = Rs.8

Cost of painting 3200m² of outer surface area= Rs.(8 × 3200)

=) Rs.25600