Question

A cuboidal tin box open at the top has dimensions 20cm×16cm×14cm . What is the total area of the metal sheet required to make 10 such boxes in square meters ?

Answer 1

AnswEr :

As we have to Find the Metal Sheet Required to make 10 Cuboidal Tin Box. For that we will find TSA of 1 Cuboidal Tin Box.

Given Dimensions Are :

• Length = 20 cm
• Breadth = 16 cm
• Height = 14 cm

• Total Surface Area of Cuboidal Box :

⇒ TSA = 2(lb + bh + hl)

⇒ TSA = 2(20 × 16 + 16 × 14 + 14 × 20)

⇒ TSA = 2(320 + 224 + 280)

⇒ TSA = 2 × 824

⇒ TSA = 1648 cm²

• Total Area of Metal Sheet Required :

⇒ Total Sheet Required = TSA × Boxes

⇒ Total Sheet Required = 1648 cm² × 10

⇒ Total Sheet Required = 16480 cm²

we have to change it into m² accrⁿ Question

⇝ 16480 cm²

⇝ 16480 /100 × 100 m²

⇝ 1648 /1000 m²

⇝ 1.648 m²

∴ 1.648 m² Metal Sheet Required for 10 Box

Answer 2

$\bold{Given}\begin{cases}\underline{\footnotesize\sf{\star\:\:Dimensions\:of\:the\:cuboidal\:tin\:box}}\\\sf{Length(l)=20cm}\\\sf{width(b)=16cm}\\\sf{Height(h)=14cm}\\ \sf{\footnotesize\sf{Find\:cost\:of\:metal\:sheet\:used\:to\:make\:10\:such\:boxes}}\end{cases}$

$\LARGE\bold\star\underline{\underline\textbf{Formula\:used}}$

• TSA of open cuboid box = TSA of cuboidal box - Area of Rectangle = 2(lb+bh+hl) - l×b

$\Large\underline{\underline{\sf{Solution}:}}$

putting values we get TSA of tin box :-----

→ TSA = 2(20×16+16×14+14×20)

→ TSA = 2(320+224+280)

→ TSA = 2 × 824

→ TSA = 1648cm²

Now, Surface Area of outer Rectangle :--

→ length × breadth = 20×16 = 320cm²

Hence ,

Total surface of open cuboidal box = 1648-320 = $\red{\bold{1328cm^{2}}}$

_________________________________

Now, TSA of 10 such boxes = 10×1328 = $\pink{\bold{13280cm^{2}}}$

Now , we have to Find in m².

we know that 10000cm² = 1m²

so, 13280cm² = 13280/10000 = 1.328m²

Hence, TSA of 10 such boxes in m² will be $\pink{\bold{1.328m^{2}}}$

$\large\underline\textbf{Hope it Helps You.}$