Question

(i)The cost of constucting a wall 8 m long , 4m high and 20 cm thick at rate of rs 25 per m^3 is
(ii)A cube whose volume is 1/8 cubic cm is placed on top of a cube whose volume is 1 cm ^3.the 2 cubes are then placed on top of a 3rd cube whose vol is 8 cm^3.the height of stacked cubes is
(iii)the number of cubes of side 3 cm that can be cut froma cuboid of dimensions 10 cm *9cm*6 cm is
answer all

Answer 1

1. given l=8m, h=4m and b=20/100 = 1/5m
    then volume of wall = lbh
                                   = 8×4×1/5
                                   = 32/5
                                   = 6.2m³
given per m³ = 25 rs
        per 6.2m³ = 6.2×25
                         = 160 Rs
3. n×volume of cube= volume of cuboid
    n×a³=lbh
    n = 10×9×6/3³
       = 10×9×6/27
       = 20 cubes
2. we know that in cube all sides are equal .so the length of side is height
   given for first cube volume = 1/8cm³
          i.e., a³=1/8
                 a = 1/2cm
i.e., height of 1st cube is 1/2 cm
   given for second cube volume a³=1
                                                    a = 1 (a is not -1 because heights are never calculate in negative)
so height of second cube is 1cm
then given volume of third cube is 8 cm³
  a³=8
  a= 2 cm
so height of third cube is 2cm
then the height of resulting staked cubes is sum of the hieghts of three cubes
              = 1/2 + 1+2
              = 1+2+4/2                (by taking lcm)
              = 7/2
              = 3.5 cms

Answer 2

1-   length of wall = 8 m
   breadth of wall = 20cm = 0.2 m
    height of wall = 4m

    vol. of wall = lbh
                =( 8 x 4 x 0.20 )m³
                =6.4 m³
    cost of building = Rs (6.4 x 25)
                       = Rs 160

2-   height of cube whose vol. is 1/8 cm³
  side³ = 1/8
side = ∛1/8
side=1/2 = 0.5 cm

 height of cube whose vol. is 1 cm³
side³ = 1
side = ∛1
side = 1 cm

height of cube whose vol. is 8 cm³
side³ = 8
side = ∛8
side = 2

total height = (0.5 +1+2) = 3.5cm

3-vol. of cuboid = (10 x 9 x 6 ) cm³ = 540cm³
vol of cube =(3)³ cm³

no of cubes that can be cut = 540/27
                                         =20 cubes