Volume and Surface Area Questions

Let original length = x and original breadth = y.

Original area = xy.

New length = x/2 and New breadth = 3y.

New area = (x/2 * 3y) = (3/2 )xy

Therefore,  Increase % = [(1/2)xy * (1/xy) * 100] % = 50%

Number of books that can be placed in the larger box is given by Volume of Box / Volume of book.
Now, n = 25 x 42 x 60 / 7 x 6 x 5
= 63000 / 210
= 300.
Therefore, 300 books can be in that box.

It takes four of those little squares -- each one 1/2 inch on a side -- to cover one square inch. That's because each one is 1/2 x 1/2, or 1/4 of a square inch.
In a rectangle that is 48 inches by 48 inches, there are 2304 square inches.(1 ft = 12 inches)
Since it takes 4 little squares to cover 1 sq inch, then it would need 2304 x 4 squares (1/2 inch on a side each) to cover a rectangle 4 feet by 4 feet.

That is 9,216 of those squares.

Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. 

Area of each tile = (41 x 41) sq.cm 

Required number of tiles = 1517 x (902/41) x 41 = 814

Slant surface of a pyramid=1/2 perimeter of base slantheight

=1/2 x (4  x Side of squarebase) x Slantheight

 The formula to find the volume is given by just multiplying Length, Breadth and Height of that object. 

 Thus, V = L x B X H  

Volume Formulae :   

1. Volume of Cube of side 's' = s x s x s = s3  cubic units.   

2. Volume of Cylinder = πR2h cubic units.  

[Where R is Radius and h is height]

Let breadth = x metres.

Then, length = (x + 20) metres.

Perimeter = 5300 m = 200 m. 26.50

2[(x + 20) + x] = 200

2x + 20 = 100

2x = 80

x = 40.

Hence, length = x + 20 = 60 m.

Volume of water displaced = (3 x 2 x 0.01) = 0.06 cu.m. 

Mass of man = Volume of water displaced x Density of water

 = (0.06 x 1000) kg

 = 60 kg.