What are the dimensions (length, breadth and height, respectively) of a cuboid with volume 720 cu cm, surface area 484 sq cm and the area of the base 72 sq cm?

Surface area of 1 brick
= 2 (lb + bh + lh)
= 2(22.5 x 10 + 10 x 7.5 + 7.5 x 22.5)
= 2(225 + 75 + 168.75)
= 2 x 468.75 = 937.50 cm²
= 93750/(100 x 100) = 0.09375 sq m
? Number of bricks = Total area/Surface area of 1 brick
= 9.375 / 0.09375 = 100

Capacity of tank = = 50000 L = 50 m³ [? 1L = 1/1000 m³ ]
? Breadth = 50/(2.5 x 10) = 2 m

Given, lb = 120 sq cm., bh = 72 sq cm, lh = 60 sq cm.
? lb x bh x lh = 120 x 72 x 60
? (lbh)² = 120 x 72 x 60
? lbh = ?120 x 72 x 60
= ?12 x 10 x 12 x 6 x 10 x 6
= 12 x 10 x 6 = 720 cm³

Let length, breadth and height be 4k, 3k and 2k, respectively.
Whole surface area = 2(lb + bh + lh)
? (lb + bh + lh) = 8788/2 = 4394
? (4 x 3 + 3 x 2 + 2 x 4 ) k² = 4394
? 26k² = 4394
? k² = 169
? k = 13
? Length = 4k = 4 x 13 = 52 cm

Surface area of cube which can be painted = 6(Side)² = 6(2)² = 24 cm²
Now, surface area of cuboid which can be painted
= 2(lb + bh + lh)
= 2(2 + 6 + 3) = 22 cm
Total surface area of both cube and cuboid
= 22 + 24 = 46 cm² < 54 cm²
Therefore, both cube and cuboid can be painted.

Let the edge of a square be x. and sum of its edges = 12 x
Now, by condition, x³ = 12x
? x(x² - 12) = 0
? Its total surface area = 6x² = 6(12) = 72 sq units

Here, x = y = -19%
According to the formula,
Percentage decrease in surface area
= [x + y + xy/100]%
= [- 19 - 19 + (-19) x (-19) /100]%
=[-38 + 361/100]%
= [-38 + 3.61]% = -34.39 %

Here, k = 12%
According to the formula,
Percentage increase in volume = [(1 + k/100)³ - 1] x 100%
= [(1 + 12/100)³ - 1] x 100%
= [(1.12)³ - 1] x 100%
= 0.404928 x 100% = 40.4928%

Given, r = 7 cm, h = 80 cm
Volume = ?r²h = (22/7) x 7 x 7 x 80
= 12320 cm³

Total surface area of cylinder = 2?r(h + r)
Given that, r = 14/2 = 7 cm, h = 40 cm
? Required total surface area = 2 x (22/7) x 7 x (40 + 7)
= 44 x 47 = 2068 sq cm