Question

. The dimensions of a metallic cuboid are 100 cm X70 cm X49 cm. It is melted and recast into a cube. Find the total surface area of the cube?

Answer 1

$\huge\underbrace\mathfrak \red{ANSWER }$

$Total\: Surface\: Area \: of \: the \: cube\\ = 38400\:cm^{2}$

$Lateral\: Surface\: Area \: of \: the \: cube \\=25600\:cm^{2}$

Step-by-step explanation:

Dimensions of a metallic cuboid :

Length (l)=100cm,

Breadth (b)=80cm,

Height (h)=64cm,

Let the edge of a cube = a cm

According to the problem given,

If metallic cuboid melted and recast into a cube.

Volume of a cube = volume of the cuboid

=> a³ = 100cm × 80cm ×64cm

=> a³ = 10×10×10×8×8×8 cm³

a = \sqrt[3]{10^{3}\times 8^{3}\times (cm)^{3}}

\implies a = 10 \times 8\:cm

$Now, Total\: Surface\: Area \: of \: the \: cube = 6a^{2}\\=6\times (80\:cm)^{2}\\=6 \times 6400 \:(cm)^{2}\\=38400\:cm^{2}--(2)$

$Now, Lateral\: Surface\: Area \: of \: the \: cube = 4a^{2}\\=4\times (80\:cm)^{2}\\=4 \times 6400 \:(cm)^{2}\\=25600\:cm^{2}--(3)$

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