A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are ? 70. What is the rate of painting per square centimetre?

Volume of the sphere = Volume of the water displaced
Let the required height to which the water rises be h.
Then, ?r₁²h = 4/3 ?r₂³
? 16 h = 4/3 x 27 ? h = 36/16 = 9/4 cm

Volume of the spherical ball = Volume of the water displaced
? 4/3 ?r³ = ?(12)² x 6.75
? r³ = 144 x 6.75 x 3/4 = 729
? r = 9 cm

From the formula the net change in volume is given as [x + y + z + (xy + yz + zx)/100 + xyz/(100)² ] %
Here, x = 200, y = z = -50 (-ve sign for decrease)
= [ 200 + (-50) + (-50) + (200) x (-50) + (-50) x (-50) + (-50) x (200)/100 + (200) x (-50) x (-50)/(100)² ] %
= 100 + (-10000 + 2500 - 10000)/100 + 500000/100 x 100 ] %
= [ 100 + (-17500)/100 + 50]%
= (150 - 175)% = -25% (-ve sign implies for a decrease )
So, the volume is decreased by 25%.

The net decrease in the surface area of the cube is given by
[x + y + xy/100] %
Here, x = y = 19%
= [-19 + (-19) + (-19) x (-19)/100] %
= [-38 + 361/100] %
= [-38 + 3.61] %= -34.39% (-ve sign implies for decrease)

The decrease in volume is given [ x + y + xy/100 ] %
Here , x = y = -24
= [(-24) + (-24) + (-24) x (-24)/100] %
= [-48 + 576/100] % = -48 + 5.76 = - 42.24 %
(-ve sign denotes decrease in volume)

Number of boxes = (Volumes of wooden box in cm³) / (Volume of 1 small box)
= (800 x 700 x 600) / (8 x 7 x 6) = 1000000

Let length = 6k, breadth = 5k and height = 4k in cm
? 2(6k x 5k + 5k x 4k + 6k x 4k) = 33300
? 148k² = 33300
? k² = 33300/148 = 225
? k = 15
? Length = 90 cm, Breadth = 75 cm, Height = 60 cm

? ?3a = 8?3
? a = 8
? Surface area = 6a²
= (6 x 8 x 8) cm²
= 384 cm²

? l² + b² = (10)² = 100
And l² + b² + h² = (10?300)² = 200
? h² = (200 - 100) = 100
? h = 10 m

? ?3 a = 14 x ?3
? a = 14
? Volume of the cube = (14 x 14 x 14)cm³
= 2744 cm³