Question

The dimensions of a cuboid are in the ratio 3:2:2 and the lateral surface of cuboid is 2000 sq.m . The outer surface of the cuboid is painted with coloured enamel at the rate of Rs 8 per sq.m . Find the total cost of painting the outer surface of the cuboid

Answer 1

Given :

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

• Outer surface of the cuboid is painted with coloured enamel at the rate of Rs 8 per m².

Find :

Total cost of painting the outer surface of the cuboid

Solution :

Let the -

• length of cuboid = 3x
• breadth of cuboid = 2x
• height of cuboid = 2x

$\boxed{\sf{Lateral \:surface\:area\:of\:cuboid\:=\:2h(l\:+\:b)}}$

Substitute the known values in above formula

=> 2000 = 2(2x)[3x + 2x]

=> 2000 = 4x(5x)

=> 2000 = 20x²

=> x² = 100

=> x = 10

$\therefore$ $\sf{Length \:of\:cuboid}$ = 3x

=> 3(10)

=> 30m

$\sf{Breadth \:of\:cuboid}$ = 2x

=> 2(10)

=> 20m

$\sf{Height \:of\:cuboid}$ = 2x

=> 2(10)

=> 20m

Now,

$\boxed{\sf{Total \:surface\:area\:of\:cuboid\:=\:2(lb\:+\:bh\:+\:hl)}}$

Substitute the known values in above formula

=> 2[(30)(20) + (20)(20) + (20)(30)]

=> 2(600 + 400 + 600)

=> 2(1600)

=> 3200 m²

Cost of painting Rs. 8 per m² = 3200 × 8

=> Rs. 25600

Answer 2

SOLUTION:-

Given:

• The dimensions of a cuboid are in the ratio 3:2:2 & the lateral surface of cuboid is 2000m².
• The outer surface of the cuboid is painted with coloured enamel at the rate of Rs.8/m².

To find:

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

Explanation:

• Let the length of a cuboid=3R m
• Let the breadth of a cuboid=2R m
• Let the height of the cuboid=2R m

&

We know that, the lateral surface area of the cuboid;

⇒2(length+breadth)×height

Therefore,

⇒ 2(3R+2R)×2R=2000

⇒ (2R+2R)×2R=$\frac{2000}{2}$

⇒ 5R×2R = 1000

⇒ 10R² = 1000

⇒ R² =$\frac{1000}{10}$

⇒ R² = 100

⇒ R =√100

⇒ R = 10m

Now,

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

Formula:Total surface area of the cuboid;

=2[lb+bh+lh] sq. units

⇒2[30×20+20×20+20×30]

⇒2[600+400+600]

⇒2[1600]

⇒3200m²

Now,

The cost of 1m² area=Rs.8

The cost of 3200m² area=Rs.(8×3200)=Rs.25600.