Question

Lovely Sweet House was placing an order for making cardboard boxes for packing
their sweets. Two sizes of boxes were required. The bigger box is of dimensions
30 cm x 20 cm x 5 cm and the smaller box of dimensions 15 cm x 12 cm x 5 cm. For all
the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard
is 5 for 1000 cm?, find the cost of cardboard required for supplying 500 boxes of each
kind.
the answer should be ₹6116.25​

Answer 1

Given :

• Dimensions of bigger box = 30 cm × 20 cm × 5 cm
• Dimensions of smaller box = 15 cm × 12 cm × 5 cm

To Find :

• The cost of cardboard required for supplying 500 boxes of each kind = ?

Solution :

★ Finding the Total surface area of bigger box :

• TSA of bigger box = 2(lb + bh + hl)

Here,

• Length (l) = 30 cm
• Breadth (b) = 20 cm
• Height (h) = 5 cm

★ Now, plug in the given values in above formula :

→ TSA of bigger box = 2(30 × 20 + 20 × 5 + 5 × 30)

→ TSA of bigger box = 2(600 + 100 + 150)

→ TSA of bigger box = 2(850)

→ TSA of bigger box = 1,700 cm²

• Hence,the surface area of bigger box is 1,700 cm².

★ 5% of the total surface area is required extra :

➝ 5% extra for bigger box = 5/100 × 1,700

➝ 5% extra for bigger box = 5 × 17

➝ 5% extra for bigger box = 85 cm²

★ Therefore, cardboard required for one big box :

➻ cardboard required for one big box = TSA of bigger box + 5% extra for bigger box

➻ cardboard required for one big box = 1,700 + 85

➻ cardboard required for one big box = 1,785 cm²

★ Similarly,find the Total surface area of smaller box :

• TSA of smaller box = 2(lb + bh + hl)

Here,

• Length (l) = 15 cm
• Breadth (b) = 12 cm
• Height (h) = 5 cm

★ Now, plug in the given values in above formula :

⟹ TSA of smaller box = 2(15 × 12 + 12 × 5 + 5 × 15)

⟹ TSA of smaller box = 2(180 + 60 + 75)

⟹ TSA of smaller box = 2(315)

⟹ TSA of smaller box = 630 cm²

• Hence,the surface area of smaller box is 630 cm².

★ 5% of the total surface area is required extra :

➺ 5% of extra for smaller box = 5/100 × 630

➺ 5% of extra for smaller box = 5/10 × 63

➺ 5% of extra for smaller box = 315/10

➺ 5% of extra for smaller box = 31.5 cm²

★ Therefore, cardboard required for one small box :

➵ cardboard required for one small box = 630 + 31.5

➵ cardboard required for one small box = 661.5 cm²

★ Therefore, TSA of cardboard required for 500 box of each kind :

➛ TSA of cardboard required for 500 box of each kind = cardboard required for one big box + cardboard required for one small box

➛ TSA of cardboard required for 500 box of each kind = (1,785 + 661.5) × 500

➛ TSA of cardboard required for 500 box of each kind = 2,446.5 × 500

➛ TSA of cardboard required for 500 box of each kind = 1,223,250 cm²

★ Now, let's find the coast of cardboard required :

⇒Coast of cardboad required = 1,223,250 × 5/1000

⇒Coast of cardboad required = 6,116,250 ÷ 1000

⇒Coast of cardboad required = Rs. 6,116.25

• Hence,the cost of cardboard required for supplying 500 boxes of each kind is Rs. 6,116.25 .

Answer 2

Explanation

Dimensions of bigger box are:

• Length =30 cm

• breadth =20 cm

• height =5 cm

• Total surface area of the bigger box

$\sf{ = 2× (l× b+b×h+h×l)}$

$\sf{=2(30×20+20×5+30×5) cm ²}$

$\sf{=2 (600+100+150)cm ²}$

$\sf{=2×(850 )cm²}$

$\bf \implies1700 \: cm²$

Now

=>> Dimensions of smaller box are =

• Length = 15 cm
• breadth =12 cm
• height =5 cm

So

• Total surface area of the smaller box

$\sf{= 2× (l× b+b×h+h×l)}$

$\sf{=2(15×12+12×5+15×5) cm ²}$

$\sf{=2 (180+60+75)cm ² }$

$\sf{=2×(315)cm²}$

$\bf \implies630 \: cm²$

Here

• Total surface area of both boxes

$\sf{= 1700 +630 =2330 \: cm²}$

Area of all overlap = 5 % of total surface area

$\sf{= 5 × 2330 \: cm²}$

$\sf{= \frac{5}{100} × 2330}$

$= \frac{11650}{100}$

$\bf \implies116.5 \: cm ²$

We know that

• Total surface area of both boxes with area of overlap =

$\sf{=2330 + 116.5 =2446.5 \: cm²}$

Total surface area of 500 boxes

$\sf{ = 2446.5 ×500}$

$\bf \implies{1,223,250}$

• Now cost of cardboard for 1000 cm²=5

• Then cost of cardboard for 1 cm² =
• = 5 /1000 Rs

• Cost of cardboard for

$\sf = { 2446.5 ×500 = 1,223,250}$

$\sf= \frac{5 \times 1,223,250}{1000}$

$\sf{= \frac{6116250}{1000} }$

$\bf \implies₹ \: 6116.25$