Question

the side of mettalic abc is 12 cm.it is melted and formed into cuboid whose length and breadth is 18 cm and 16cm. respectively find the cuboid.​

Answer 1

Correct Question:

A metal cube of side 12cm is melted and a cuboid whose length is 18cm and breadth 16cm is formed. Find the height of the cuboid.

Answer:

The Height of the cuboid is 6 cm.

Step-by-step explanation:

Given :

Side of the cube = 12 cm

Length of the cuboid = 18 cm

Breadth of the cube = 16 cm

To find :

Height of the cuboid

Solution :

As the cube is melted and reformed into a cuboid, the volume of the cube and cuboid would be the same value.

★ Volume of cube -

$\boxed{\sf{Volume=Side^{3}}}$

$\sf{\implies} \: {12}^{3} \\ \\ \sf{\implies} \:1728 \: {cm}^{3}$

Volume of the cube = 1728 cm²

$\rule{300}{1.5}$

★ Height of the cuboid -

Let the height be h

$\boxed{\sf{Volume=Length \times Breadth \times Height}}$

$\sf{\implies} \: 1728 = 18 \times 16 \times h \\ \\ \sf{\implies} \:1728 = 288h \\ \\ \sf{\implies} \: h = \dfrac{1728}{228} \\ \\ \sf{\implies} \: h = 6$

Height = 6 cm

$\therefore$ The Height of the cuboid is 6 cm.

Answer 2

Question :-

→ Given above ↑

Answer :-

$\mapsto \boxed{ \sf \: h = 6 \: cm} \:$

Height of cuboid is 6 cm .

To Find :-

→ Height of the cuboid.

Explanation :-

According to the question ,

Assumption :-

→ A cube is melted to form a cuboid ,hence the volume of cube will be same of cuboid.

Solution :-

We have ,

• Side of the cube (a) = 12 cm

• Length of the cuboid (l) = 18 cm

• bredth of the cuboid (b) = 16 cm

Now ,

We know that ,

$\mapsto \sf \red{ volume \: of \: cuboid} \: (v_1) =\green{ l \times b \times h }\\ \\ \mapsto \sf \: v_1 =\orange{ 18 \times 16 \times h }\\ \\ \mapsto \sf \blue{ v_1 = 288} \: \times h \:$

and now ,

$\to \sf\purple{ volume \: of \: cube} (v_2)= \pink{{ \{side(a) \}}^{3}} \\ \\ \to \sf \: v_2 = {(12)}^{3} \\ \\ \to \sf \: \boxed{ \sf \red{v_2 = 1728}}$

$\sf \red{according \: to }\: our \green{ \: assumption} \: \\ \because \sf \: v_1 = v_2 \\ \\ \mapsto \sf \green{288 \times h =} 1728 \\ \\ \mapsto \sf \: h = \blue{ \frac{1728}{288} }\\ \\ \mapsto \boxed{ \sf \: h = 6 \: cm}$

therefore height of cuboid is 6 cm