Question

Quayleen wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?​

Answer 1

$\bullet\:{\boxed{\tt{\red{{Given :}}}}}$

• Length of the wooden box $(l)$ = 80cm.

• Breadth of the wooden box $(b)$ = 40cm.

• Height of the wooden box $(h)$ = 20cm.

• Side of the square sheet paper = 40cm.

$\bullet\:{\boxed{\tt{\red{{To : Find :}}}}}$

The number of sheets required.

$\bullet\:{\boxed{\tt{\red{{Formula \: \: used :}}}}}$

$\star{\underline{\boxed{{\sf{{{TSA}} = \underline{\underline{{\purple\sf 2(lb+bh+hl)}}}}}}}} \star$

$\star{\underline{\boxed{{\sf{{{Area \: of \: square}} = \underline{\underline{{\purple{\sf side \times side }}}}}}}}}\star$

$\star{\underline{\boxed{{\sf{{{Number \: of \: sheets \: required} = {{{\purple{\sf \dfrac{TSA}{area \: of \: one \: sheet}}}}}}}}}}} \star$

$\bullet\:{\boxed{\tt{\red{{Concept :}}}}}$

As Quayleen wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. So for knowing the number of sheets required, we need two things one the TSA and Area of one sheet. Once, we will get the values we will divide them to get the answer. Let's Start !!

$\bullet\:{\boxed{\tt{\red{{Solution :}}}}}$

As we know that ::

Total surface area of cuboid $\large[ \sf 2(lb+bh + hl)]$

Here,

✧ Length $(l)$ = 80cm

✧ Breadth $(b)$ = 40cm

✧ Height $(h)$ = 20cm

Now, by putting the values we get :

$\longrightarrow 2 \bigg[ (80 \times 40) + (40 \times 20) + (20 \times 80) \bigg]\sf {cm}^{2}$

$\longrightarrow 2 \bigg[ (3200) + (800) + (1600) \bigg] \sf {cm}^{2}$

$\longrightarrow 2 \bigg[ 5600 \bigg] \sf {cm}^{2}$

$\longrightarrow 11200 \: \sf {cm}^{2}$

Hence, the total surface area of the wooden box is 11200 cm²

Now,

The area of each sheet of paper will be :

$\sf \longrightarrow side \times side$

$\sf \longrightarrow (40 \times 40) \: {cm}^{2}$

$\longrightarrow \sf (1600) \: {cm}^{2}$

Hence, the area of each sheet of paper is 1600 cm²

Now,

For finding the number of sheets required

$\longrightarrow \tt \dfrac{total \: surface \: area \: of \: box}{ area \: of \: one \: sheet}$

$\longrightarrow \sf\dfrac{ \cancel{11200}_{7}}{\cancel{1600}_{1}}$

$\longrightarrow \purple{ \sf 7}$

Therefore, Quayleen requires 7 sheets.

$\rule{280pt}{2pt}$