Question

A cuboid, with dimensions L cm by 18 cm by
38 cm, has a volume of 35 568 cm.
(1) Find the length, L, of the cuboid.
(1) The cuboid is melted to form
cubes of length 2 cm. How many cubes
can be obtained?
2. An open rectangular tank, with dimensions 55 cm by 35 cm by 36 cm, is initially
hall-filled with water. Find the depth of water in the tank after 7700 cm of
water is added to it.
​

Answer 1

Step-by-step explanation:

as we know that the volume of coboidis l×b×h=35568

l×38×18=35568

l=92.24cm

Answer 2

Solution :

(1)dimensions of cuboid = L× 18× 38

volume of cuboid = 35568 cm ³

then

volume of cuboid = length × breadth × height

35568 = L× 18× 38

35568 =L×684

L = 52 cm

i.e length of the cuboid is 52 cm

now , length of cube = 2 cm

volume of cube = side³ = 2³ = 8

number of cubes obtained = $\frac{\text{volume of cuboid}}{\text{volume of 1 cube}}$

= $\frac{35568}{8}$

= 4446

hence , 4446 cubes are obtained

(2) volume of tank when it is half filled

i.e height of the tank will be half = 18 cm

length = 55 cm

breadth = 35 cm

volume of tank when it is half filled  = 55×35×18 = 34650 cm³

total volume after 7700 cm³ is added to it

total volume of the tank = 7700 + 34650 = 42350 cm³

volume of tank = 42350 cm³

length × breadth × depth = 42350 cm³

55× 35× depth = 42350 cm³

1925× depth = 42350 cm³

depth = 22  cm

hence , The depth of the tank = 22 cm

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