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
Answers
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)