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How many soap cakes can be placed in a box of size $56 cm × 0.4 m ×$ $0.25 m$ , if the size of a soap cake is $7 cm × 5 cm × 2.5 cm ?$

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100

440

230

640

answer is D.

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Detailed Solution

It is given box of size

56 cm × 0.4 m ×

0.25 m

and size of a soap cake is

7 cm × 5 cm × 2.5 cm

.
We know that the volume of the cuboid,

V = l × b × h

The size of the box is

56 c m × 0.4 m × 0.25 m

.
The size of the soap cake is 7

c m × 5 c m ×

2.5

c m

.
To find the number of soap cakes that can be placed in a box.
Volume of the box =

56 c m × 0.4 m × 0.25 m

We know, 1m=100 cm

⇒ V o l u m e o f t h e b o x = 56 c m × 0.4 × 100 c m × 0.25 × 100 c m ⇒ V o l u m e o f t h e b o x = 56 c m × 40 c m × 25 c m ⇒ V o l u m e o f t h e b o x = 56000 c m 3

Volume of the soap cake is,

⇒ V o l u m e o f t h e s o a p c a k e = 7 c m × 5 c m × 2.5 c m ⇒ V o l u m e o f t h e s o a p c a k e = 87.5 c m 3

The number of soap cakes is given by the formula,
Number of soap cakes =

V o l u m e o f b o x V o l u m e o f s o a p c a k e

⇒ N u m b e r o f s o a p c a k e s = 56000 87.5 ⇒ N u m b e r o f s o a p c a k e s = 640

The number of soap cakes that can be placed in a box is 640.
Hence option (4) is correct.

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