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How many soap cakes each measuring $7 × 5 × 2.5$ cm can be placed in a box of size $56 × 40 × 25$ cm?

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640

230

650

260

answer is A.

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Detailed Solution

Given that,
Length of box,

l = 56 c m

Breadth of box,

b = 40 c m

Height of box,

h = 25 c m

Length of soap cake,

L = 7 c m

Breadth of soap cake,

B = 5 c m

Height of soap cake,

H = 2.5 c m

We know that, volume of box,

V = l × b × h

.
Substituting the value of

l = 56 c m

b = 40 c m

and

h = 25 c m

in above formula we get,

V = 56 c m × 40 c m × 25 c m

V = 56000 c m 3

…………………. (1)
Substituting the value of

l = 7 c m

b = 5 c m

and

h = 2.5 c m

in above formula we get,

V = 7 c m × 5 c m × 2.5 c m

V = 87.5 c m 3

……………….. (2)
Since, total number of soaps placed in box

= V o l u m e of  box v o l u m e of each soap cake

,
We get,
Total number of soaps placed in box,

= 56000 c m 3 87.5 c m 3

= 640

Hence, 640 soap cakes can be placed in the box.
Therefore, option 1 is correct.

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