Question

960 identical packets of soaps each of 10 cm long and 5 cm wide can be kept inside a rectangular box of dimension 80 cm*60 cm*40 cm, what is the height of each packet of soap?

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Answer 1

Answer :-

$\: \: \boxed{\sf{\blue{Let's \: understand \: the \: concept \: first \: }}}$

Here the concept of Volume of Cuboid has been used. We know that the packets of soap are in shape of cuboid. Now if, the total number of packets each if same dimensions, are packed in a a box, then the volum of box will be equal to the number of packets of soap into the volume of each soap. Using this concept, let us find our answer.

$\: ➮ \: \large{\underline{\boxed{\rm{\green{Volume \: of \: Cuboid \: = \: Length(L) \: \times \: Breadth(B) \: \times \: Height(H)}}}}}$

$\: ➮ \: \large{\underline{\boxed{\rm{\green{Volume \: of \: box \: = \: Volume \: of \: each \: packet \: \times \: Number \: of \: packets}}}}}$

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★ Question :-

960 identical packets of soaps each of 10 cm long and 5 cm wide can be kept inside a rectangular box of dimension 80 cm*60 cm*40 cm, what is the height of each packet of soap ?

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★ Solution :-

Given,

» Number of packets of soap = n = 960

» Length of each packet of soap = l = 10 cm

» Breadth of each packet of soap = b = 5 cm

» Length of each packet of soap = L = 80 cm

» Breadth of each packet of soap = B = 60 cm

» Height of each packet of soap = H = 40 cm

• Let the height of the packet of soap be 'h' cm. Then, using the concept, we get,

⟹ l × b × h × n = L × B × H

⟹ 10 × 5 × h × 960 = 80 × 60 × 40

⟹ 50 × 960 × h = 80 × 60 × 40

$\: \: \: \: \huge{\longrightarrow \:\:\bold{h \: = \: \dfrac{80 \: \times \: 60 \: \times \: 40}{50 \: \times \: 960}}}$

⟹ h = 4 cm

$\: \: ➮ \: \: \underline{\boxed{\sf{\red{Hence, \: the \: height \: of \: each \: packet \: of \: soap \: is \: \underline{4 \: cm}}}}}$

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$\: \: \boxed{\rm{\purple{Have \: a \: glimpse \: here \: for \: better \: understanding \: }}}$

• Volume of cuboid = (side)³

• Volume of cylinder = πr²h

where, r is radius and h is height.

• Volume of cone = ⅓(πr²h)

• Total Surface Area of Cuboid = 2(lb + bh + lh)

• Total Surface Area of Cube = 4a²

• Total Surface Area of cylinder = 2πr(r + h)

• Total Surface Area of Cone = πr(r + l)

Answer 2

Given :

• 960 identical packs of soaps each of 10 cm long and 5 cm wide can be kept in a rectangular box of 80 cm * 60 cm * 40 cm.

To find :

• Height of each packet.

Solution :

Now as 960 packets of soap can be kept inside that cartoon, so :

Volume(cartoon) = n * Volume(each packet of soap)

Here, n = number of soap packets.

Let the height of each packet of soap be x cm.

Volume of cartoon = l * b * h

Volume of each packet of soaps = l * b * h

According to question,

⇒ 80 * 60 * 40 = 960 * 10 * 5 * x

⇒ 192000 = 48000 * x

⇒ x = 192000/48000

⇒ x = 4 cm

∴ Height of each packet of soap = 4 cm