Question

A cuboidal block of ice cream measuring 12 x 8 x 6 cm is cut into cubes ideal pieces measuring 2 hours into 2 into 1 cm how many pieces will be formed

Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Areas of Cuboid has been used. According to this, we know thag dimensions of block has been given. We can then find its volume. Also we are given the cuboidal blocks into which the pieces are made. We can find its volume also. Then we can divide tot volume of block by volume of each piece to find number of pieces formed because volume will be divided into pieces .

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★ Formula Used :-

$\: \: \large{\boxed{\boxed{\sf{Area \: of \: Cuboid \: = \: \bf{Length(L) \: \times \: Breadth(B) \: \times \: Height(H) }}}}}$

$\: \: \\ \large{\boxed{\boxed{\sf{Number \: of \: pieces \: formed \: = \: \bf{\dfrac{Volume \: of \: Intitial \: block}{Volume \: of \: each \: final \: piece}}}}}}$

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★ Question :-

A cuboidal block of ice cream measuring 12 x 8 x 6 cm is cut into Cuboidal ideal pieces measuring 2 cm into 2 into 1 cm. How many pieces will be formed ?

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★ Solution :-

Given,

» Dimensions of Cuboidal Block = 12 cm × 8 cm × 6 cm

» Dimensions of each smaller Cuboidal pieces = 2 cm × 2 cm × 1 cm

Then according to the given question :-

~ Volume of Cuboidal Block :-

➣ Volume of Cuboidal block = 12 cm × 8 cm × 6 cm

➣ Volume of Cuboidal block = 576 cm³

$\: \\ \qquad \qquad \large{\boxed{\boxed{\sf{Volume \: of \: Cuboidal \: block \: = \: \bf{576 \: cm^{3}}}}}}$

~ Volume of Each Cuboidal Smaller Pieces :-

➣ Volume of each smaller Cuboidal pieces = 2 cm × 2 cm × 1 cm

➣ Volume of each smaller Cuboidal pieces = 4 cm³

$\: \\ \qquad \qquad \large{\boxed{\boxed{\sf{Volume \: of \: each \: smaller\: Cuboidal \: pieces \: = \: \bf{4 \: cm^{3}}}}}}$

~ Number of pieces :-

$\: \large{\tt{\Longrightarrow \: \: Number \; of \; pieces \; formed \; = \; \bf{\dfrac{Volume \: of \: Intitial \: block}{Volume \: of \: each \: final \: piece}}}}$

$\: \\ \large{\tt{\Longrightarrow \: \: Number \; of \; pieces \; formed \; = \: \bf{\dfrac{576 \: \not{cm^{3}}}{4 \: \not{cm^{3}}}} \: \: = \: \: \bf{144}}}$

➣ Number of pieces formed = 144 pieces

$\: \\ \large{\boxed{\boxed{\sf{Number \: of \: pieces \: formed \: = \: \bf{\underline{144 \: pieces}}}}}}$

$\: \\ \large{\boxed{\rm{\mapsto \: \: Thus, \: the \: number \: of \: pieces \: formed \: are \: \boxed{\bf{144 \: pieces}}}}}$

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$\: \: \underline{\overline{\large{\sf{Let's \: understand \: more \: formulas\: :-}}}}$

• Volume of cube = (Side)³

• Volume of cylinder = πr²h

• Volume of Cone = ⅓ × πr²h

• TSA of Cube = 6 × (Side)²

• TSA of Cylinder = 2πr² + 2πrh

• LSA of Cube = 4 × (Side)²

• LSA of Cylinder = 2πrh

• LSA of Cone = πrl

Answer 2

Correct question :-

A cuboidal block of ice cream measuring 12 x 8 x 6 cm is cut into small cuboid pieces measuring 2 into 2 into 1 cm how many pieces will be formed

?

Given :

• Dimensions of cuboidal block = 12 * 8 * 6 cm
• Dimensions of small cuboid pieces = 2 * 2 * 1

To find :

• Number of pieces formed

Solution :

At first finding volume of cuboidal block :

Volume of cuboid = l * b * h

⇒  Volume of cuboidal block = 12 * 8 * 6

⇒  Volume of cuboidal block = 576 cm³

Now volume of small cuboid pieces :

⇒  Volume of cuboid pieces = 2 * 2 * 1

⇒  Volume of cuboid pieces = 4 cm³

Now we know,

Number of pieces = Volume of cuboidal block/Volume of cuboid pieces

⇒  Number of pieces = 576/4

⇒  Number of pieces = 144

Therefore,

144 pieces of small cuboids will be formed.