If the length breadth and the height of cuboid are in the ratio 6 :5 : 4 and if the total surface area is 33300 cm ², then the length, breadth and height in cm. are respectively?

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

As the box is painted from inside, the dimensions of the box from inside are
Length = (21 - 05 - 05) = 20 cm
Breadth = (11 - 05 - 05) = 10 cm and height = (6 - 05) = 5.5
Total number of faced to be painted = 4 walls + One base
The dimensions of two of the walls = 2 x (10 x 5.5)
The dimensions of the remaining two = 2 x (20 x 5.5) and that of the base = (20 x 10 ) and so the total area to be pained = 2 x (10 x 5.5) + 2 x (20 x 5.5) + (20 x 10 ) = 530cm³
Since, the total expenses of painting this area is ?70, the rate of painting
= 70/530 = 0.13 = ? 0.1 per cm³ (approx)

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%.

? ?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

Length of pencil = ? [(8)² + (6)² + (2)²] cm
= ?104 cm
= 2?26

Speed per min = (3 x 1000)/60 m = 50 m
Volume of water running per min. = (45 x 2 x 50) m²
= 4500 m³