Question

Three iron cuboids of dimensions 3 cm x 2.5 cm x 4 cm, 3.5 cm x 2 cm x 2.5 cm and 4 cm x 3 cm
x 1.5 cm are melted to form a cube of edge 4 cm. How much iron would be lost to make it?
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Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Loss\:of\:iron=1.5\:cm}^{3}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ \text{Dimension \: of \: iron cuboids} \\ : \implies \text{Cuboid}_{1} = 3 \times 2.5 \times 4 \\ \\ : \implies \text{Cuboid}_{2} = 3.5 \times 2\times 2.5 \\ \\ : \implies \text{Cuboid}_{3} = 4\times 3 \times 1.5 \\ \\ : \implies \text{Edge \: of \: cube = 4 \: cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ \implies \text{Iron \: loss \: in \: making \: cube \: of \: edge \: 4cm = ?}$

• According to given question :

$: \implies \text{Volume \: of \: cuboid}_{1} = 3 \times 2.5 \times 4 \\ \\ : \implies \text{Volume \: of \: cuboid}_{1} = 30 {cm}^{3} \\ \\ \bold{Similarly,} \\ : \implies \text{Volume \: of \: cuboid}_{2} = 17.5 {cm}^{3} \\ \\: \implies \text{Volume \: of \: cuboid}_{3} =18 {cm}^{3} \\ \\ \bold{For \: volume \: of \: cube} \\ : \implies Volume \: of \: cube = {a}^{3} \\ \\ : \implies Volume = {4}^{2} \\ \\ : \implies \text{Volume = 64} {cm}^{3} \\ \\ \bold{For \: loss \: of \: iron } \\ : \implies Loss \: of \: iron = volume \: of \: (cuboid_{1} + cuboid_{2} + cuboid_{3} )- Volume \: of \: cube \\ \\ : \implies \text{Loss \: of \: iron = 30 + 17.5 + 18 - 64} \\ \\ : \implies \text{Loss \: of \: iron = 65.5 - 64 }\\ \\ \green{ : \implies \text{Loss \: of \: iron = 1.5 \: } {cm}^{3}}$

Answer 2

Question :-- Three iron cuboids of dimensions 3 cm x 2.5 cm x 4 cm, 3.5 cm x 2 cm x 2.5 cm and 4 cm x 3 cm

x 1.5 cm are melted to form a cube of edge 4 cm. How much iron would be lost to make it ?

Formula used :--

→ Volume of Cuboid = Length * Breadth * Height

→ Volume of cube = (side)³

→ Loss of iron = (volume of all three cuboids) - (volume of cube) . [ as when melted From volume of all cuboids a cube was formed and rest is left. ]

__________________________

Solution :--

Putting all values in above Formula we get,

→ Volume of cuboid 1 = 3 * 2.5 * 4 = 30cm³

→ Volume of cuboid 2 = 3.5*2*2.5 = 17.5cm³

→ Volume of cuboid 3 = 4*3*1.5 = 18cm³

So, Volume of all three cuboid that was melted = 30 + 17.5 + 18 = 65.5cm³ ..

__________________________

Now, let see volume of cube that was required to Make a cube :--

→ Volume of cube = (a)³ = (4)³ = 4*4*4 = 64cm³ ..

So,

→ iron would be lost to make cube will be = 65.5 - 64

= 1.5cm³ ..

Hence, when we make a cube out of melted iron we get a cube of side 4cm and 1.5cm³ iron will be left ..