Question

Find the number of cakes of soap each measuring 9 cm x 5 cm x 2 cm that can be placed in a big cuboidal box measuring 1.5 m x 0.9 m x 0.5 m.​

Answer 1

Answer :-

$\:\\\large{\boxed{\sf{Firstly,\;let's\;understand\;the\;concept\;used\;:-}}}$

Here the concept of Volume of Cuboid had been used. First we can find the Volume of Box and then we can find the volume of each soap. After that we cab divide the volume of box by volume of each soap to find the number of soaps required, since volume can neither be created nor be destroyed.

Let's do it !!

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★ Formula Used :-

$\:\\\large{\boxed{\sf{Volume\;of\;Cuboid\;=\;\bf{Length\:\times\:Breadth\:\times\:Height}}}}$

$\:\\\large{\boxed{\sf{Number\;of\;soap\;cakes\;=\;\bf{\dfrac{Volume\;of\;box}{Volume\;of\;each\;soap\;cake}}}}}$

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★ Question :-

Find the number of cakes of soap each measuring 9 cm x 5 cm x 2 cm that can be placed in a big cuboidal box measuring 1.5 m x 0.9 m x 0.5 m.

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★ Solution :-

Given,

» Dimensions of box = 1.5 m × 0.9 m × 0.5 m

= 150 m × 90 m × 50 m

» Dimensions of each soap cake

= 9 cm × 5 cm × 2 cm

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~ For the Volume of Box :-

$\:\\\qquad\large{\sf{:\longrightarrow\;\;\:Volume\;of\;Cuboid_{(Box)}\;=\;\bf{Length\:\times\:Breadth\:\times\:Height}}}$

$\:\\\qquad\large{\sf{:\longrightarrow\;\;\:Volume\;of\;Cuboid_{(Box)}\;=\;\bf{150\:\times\:90\:\times\:50\;\:=\;\:\underline{\underline{675000\;\;cm^{3}}}}}}$

$\:\\\large{\boxed{\boxed{\tt{Volume\;of\;box\;=\;\bf{675000\;\;cm^{3}}}}}}$

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~ For the Volume of Each Soap Cake :-

$\:\\\qquad\large{\sf{:\longrightarrow\;\;\:Volume\;of\;Cuboid_{(Each\:soap\:cake)}\;=\;\bf{Length\:\times\:Breadth\:\times\:Height}}}$

$\:\\\qquad\large{\sf{:\longrightarrow\;\;\:Volume\;of\;Cuboid_{(Each\:soap\:cake)}\;=\;\bf{9\:\times\:5\:\times\:2\;\:=\;\:\underline{\underline{90\;\;cm^{3}}}}}}$

$\:\\\large{\boxed{\boxed{\tt{Volume\;of\;Each\;soap\;cake\;=\;\bf{90\;\;cm^{3}}}}}}$

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~ For the Number of Each Soap Cakes :-

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:Number\;of\;soap\;cakes\;=\;\bf{\dfrac{Volume\;of\;box}{Volume\;of\;each\;soap\;cake}}}}$

$\:\\\qquad\large{\sf{:\Longrightarrow\;\;\:Number\;of\;soap\;cakes\;=\;\bf{\dfrac{675000}{90}\;\:=\;\:\underline{\underline{7500}}}}}$

$\:\\\large{\underline{\underline{\rm{Thus,\;number\;of\;soap\;cakes\;required\;are\;\:\boxed{\bf{7500}}}}}}$

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★ More to know :-

• Volume of Cube = (Side)³

• Volume of Cone = ⅓ × πr²h

• Volume of Cylinder = πr²h

• Volume of Sphere = ⅔ × πr³

• Volume of Hemisphere = (4/3) × πr³

Answer 2

$\underline{\underline{\sf{\maltese\:\:Question}}}$

⭐ Find the number of cakes of soap each measuring 9 cm × 5 cm × 2 cm that can be placed in a big cuboidal box measuring 1.5 m × 0.9 m × 0.5 m

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Dimensions of Soap : 9 cm × 5 cm × 2 cm

• Dimensions of Box : 1.5 m × 0.9 m × 0.5 m

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Number of soaps that can be placed in a big cuboidal box

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• No. of soap cakes = 7500

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

As already Given (Soap Dimensions) :

• Length = 9 cm
• Breadth = 5 cm
• Height = 2 cm

Volume of box = No. of soap cakes × Volume of one soap

⇒  Volume of box = No. of soap cakes × (Length × Breadth × Height)

⇒  Volume of box = No. of soap cakes × (9 cm × 5 cm × 2 cm)

⇒  Volume of box = No. of soap cakes × (90 cm³)

⇒  Volume of box = No. of soap cakes × 90 cm³

⇒  Volume of box = No. of soap cakes × 90 cm³

As already Given (Box Dimensions) :

• Length = 1.5 m
• Breadth = 0.9 m
• Height = 0.5 m

⇒  Volume of box = No. of soap cakes × 90 cm³

⇒  (Length × Breadth × Height) = No. of soap cakes × 90 cm³

⇒  (1.5 m × 0.9 m × 0.5 m) = No. of soap cakes × 90 cm³

⇒  (0.675 m³) = No. of soap cakes × 90 cm³

⇒  0.675 m³ = No. of soap cakes × 90 cm³

Convert m³ to cm³

⇒  0.675 m³ = No. of soap cakes × 90 cm³

⇒  0.675 (m × m × m) = No. of soap cakes × 90 cm³

We know 1 m = 100 cm

⇒  0.675 (100 cm × 100 cm × 100 cm) = No. of soap cakes × 90 cm³

⇒  0.675 (1000000 cm³) = No. of soap cakes × 90 cm³

⇒  0.675 × 1000000 cm³ = No. of soap cakes × 90 cm³

⇒  675000 cm³ = No. of soap cakes × 90 cm³

Dividing both sides by 90 cm³

⇒  675000 cm³/90 cm³ = (No. of soap cakes × 90 cm³)/90 cm³

⇒  675000/90  = No. of soap cakes

⇒  67500/9  = No. of soap cakes

⇒  7500  = No. of soap cakes

Switch Sides

⇒  No. of soap cakes = 7500

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