Question

Question:

Cardboard boxes of two different sizes are made. The bigger has dimensions 20 cm, 15cm, and 5cm. The smaller dimensions 16 cm, 12 cm, 4 cm. 5% of the total surface area is extra required for overlaps . If the cost of the cardboard is R.s. 20 for one square meter. Find the cost of cardboard for supplying 200 boxes of each kind?

Answer 1

♧ Given:-    

~Bigger Box

• ➛ Length = 20 cm
• ➛ Breadth = 15 cm
• ➛ Height = 5 cm

~Smaller Box

• ➛ Length = 16 cm
• ➛ Breadth = 12 cm
• ➛ Height = 4 cm

♧ To find:-          

• ➛ The cost of cardboard for supplying 200 boxes of each kind?

♧ Formula Used:-          

• $\Large\boxed{\underline{\sf{Total\:surface\:area\:_{(\:CUBIOD\:)}\:=\:2\:(\:l\:b\:+\:b\:h\:+\:h\:l\:)}}}$

where,

• ➛ l = Length
• ➛ b = breadth
• ➛ h = height

♧ Calculating:-      

Step 1: Firstly we will find out the total surface area of the cuboid of the bigger box, so we will substitute the values in the formula.

~Bigger Box

• ➛ Length = 20 cm
• ➛ Breadth = 15 cm
• ➛ Height = 5 cm

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:BIGGER\:BOX\:)}\:=\:2\:(\:l\:b\:+\:b\:h\:+\:h\:l\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:BIGGER\:BOX\:)}\:=\:2\:(\:20\:\times\:15\:+\:15\:\times\:5\:+\:5\:\times\:20\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:BIGGER\:BOX\:)}\:=\:2\:(\:300\:+\:75\:+\:100\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:BIGGER\:BOX\:)}\:=\:2\:(\:475\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:BIGGER\:BOX\:)}\:=\:950\:cm^{2}}$

. ° . The total surface area of the bigger box is 950 cm².

Step 2: Now we will find out the total surface area of the smaller box by substituting the values in the formula.

~Smaller Box

• ➛ Length = 16 cm
• ➛ Breadth = 12 cm
• ➛ Height = 4 cm

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:SMALLER\:BOX\:)}\:=\:2\:(\:l\:b\:+\:b\:h\:+\:h\:l\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:SMALLER\:BOX\:)}\:=\:2\:(\:16\:\times\:12\:+\:12\:\times\:4\:+\:4\:\times\:16\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:SMALLER\:BOX\:)}\:=\:2\:(\:192\:+\:48\:+\:64\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:SMALLER\:BOX\:)}\:=\:2\:(\:304\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:SMALLER\:BOX\:)}\:=\:608\:cm^{2}}$

. ° . The total surface area of the smaller box is 608 cm².

Step 3: Now we will find out the total surface area of 200 boxes of each type.

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:200\:BOXES\:)}\:=\:200\:(\:TSA\:of\:bigger\:box\:+\:TSA\:of\:smaller\:box\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:200\:BOXES\:)}\:=\:200\:(\:950\:+\:608\:)}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:200\:BOXES\:)}\:=\:200\:\times\:1558}$

$\qquad\tt{:\implies\:Total\:surface\:area\:_{(\:200\:BOXES\:)}\:=\:311600\:cm^{2}}$

. ° . The total surface area of the 200 boxes of each kind is 311600 cm².

Step 4: Now we will find out the extra area for overlaps.  

$\qquad\tt{:\implies\:Extra \:area\: required\: =\: 5\:\%\: of\: (\: 950\: +\: 608\: ) }$

$\qquad\tt{:\implies\:Extra \:area\: required\: =\: \dfrac{5}{100}\: \times\: 1558\:\times\:200 }$

$\qquad\tt{:\implies\:Extra \:area\: required\: =\: 5\: \times\: 1558\:\times\:2}$

$\qquad\tt{:\implies\:Extra \:area\: required\: =\:10\:\times\:1558}$

$\qquad\tt{:\implies\:Extra \:area\: required\: =\:15580\:cm^{2}}$

. ° . The extra area for overlaps is 15580 cm².    

So,

      The total cardboard required

$\qquad\tt{:\implies\:Total\:required\: =\:311600\:+\:15580}$

$\qquad\tt{:\implies\:Total\:required\: =\:327180\:cm^{2}}$

$\qquad\tt{:\implies\:Total\:required\: =\:\dfrac{327180}{1000}\:=\:327.18\:m^{2}}$

Step 5: Now, we will find out the cost of the Cardboard.

$\qquad\tt{:\implies\:Cost\:of\:cardboard\:for\:1\:m^{2}\:=\:Rs.\:20}$

$\qquad\tt{:\implies\:Cost\:of\:cadboard\:for\:327.18\:m^{2}\:=\:20\:\times\:327.18}$

$\qquad\tt{:\implies\:Cost\:of\:cadboard\:for\:327.18\:m^{2}\:=\:Rs.\:654.36}$

. ° . The cost of cardboard for supplying 200 boxes of each kind is Rs. 654.36.

♧ Answer:-      

• The cost of cardboard for supplying 200 boxes of each kind is Rs. 654.36.