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Answer 1

Question:-

A cuboid whose dimensions are 2.5 cm by 0.5 cm by 100 cm is melted and costed into a cube of edge 'x' cm. Find the edge 'x' and surface area of the cube

Solution:-

Given,

Dimensions of cuboid = 2.5 × 0.5 × 100

Here,

Volume of cuboid = Volume of Cube

$l \times b \times h = {a}^{3}$

i. e.,

$2.5 \times 0.5 \times 100 = {x}^{3}$

$25 \times 5 = {x}^{3}$

$125 = {x}^{3}$

$x = \sqrt[3]{125} = 5$

Therefore, Edge of the Cube = 5 cm

2) Surface area of Cube

$= 6 {a}^{2}$

We know that side of Cube = 5 cm

Surface area

$= 6 \times {5}^{2}$

$= 6 \times 25$

$= 150 \: {cm}^{2}$

Formulae :-

Volume of cuboid = l × b × h

Volume of cube = a^3

Surface area of cube = 6 × a^2

Answer 2

Step-by-step explanation:

Question:-

A cuboid whose dimensions are 2.5 cm by 0.5 cm by 100 cm is melted and costed into a cube of edge 'x' cm. Find the edge 'x' and surface area of the cube

Solution:-

Given,

Dimensions of cuboid = 2.5 × 0.5 × 100

Here,

Volume of cuboid = Volume of Cube

l \times b \times h = {a}^{3}l×b×h=a3

i. e.,

2.5 \times 0.5 \times 100 = {x}^{3}2.5×0.5×100=x3

25 \times 5 = {x}^{3}25×5=x3

125 = {x}^{3}125=x3

x = \sqrt[3]{125} = 5x=3125=5

Therefore, Edge of the Cube = 5 cm

2) Surface area of Cube

= 6 {a}^{2}=6a2

We know that side of Cube = 5 cm

Surface area

= 6 \times {5}^{2}=6×52

= 6 \times 25=6×25

= 150 \: {cm}^{2}=150cm2

Formulae :-

Volume of cuboid = l × b × h

Volume of cube = a^3

Surface area of cube = 6 × a^2