Q. 74.2( 382 Votes )

Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions25 cm × 20 cm × 5 cm and the smaller of dimensions 15 cm × 12 cm × 5 cm for all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs 4 for 1000 cm2, find the cost of cardboard required for supplying 250 boxes of each kind

Answer :



We know total surface area of cuboid = 2(lb + lh + bh)

For bigger box

Length of bigger box = 25 cm

Breadth of bigger box = 20 cm
Height of bigger box = 5 cm

Total surface area of bigger box = 2(lb + lh + bh)

= [2(25 × 20 + 25 × 5 + 20 × 5)] cm2

= [2(500 + 125 + 100)] cm2

= 1450 cm2

Extra area required for overlapping = 5% of the total surface area of bigger box
Extra area required for overlapping =
cm2

= 72.5 cm2

While considering all overlaps, total surface area of 1 bigger box = (1450 + 72.5) cm2

                                                                                             =1522.5 cm2

Area of cardboard sheet required for 250 such bigger boxes = (1522.5 × 250) cm2

                                                                                      = 380625 cm2

Similarly, total surface area of smaller box

= [2(15 ×12 + 15 × 5 + 12 × 5] cm2

= [2(180 + 75 + 60)] cm2

= (2 × 315) cm2

= 630 cm2


Therefore, extra area required for overlapping =  5% of the total surface area of smaller box


Therefore, extra area required for overlapping =   cm2

= 31.5 cm2

Total surface area of 1 smaller box while considering all overlaps = (630 + 31.5) cm2

= 661.5 cm2

Area of cardboard sheet required for 250 smaller boxes = (250 × 661.5) cm2

= 165375 cm2

Total cardboard sheet required

= (380625 + 165375) cm2

= 546000 cm2

Cost of 1000 cm2 cardboard sheet = Rs 4

Cost of 546000 cm2 cardboard sheet

=  

= Rs 2184


Therefore, the cost of cardboard sheet required for 250 such boxes of each kind will be Rs 2184

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Smart Revision | Surface Areas and Volume of SolidsSmart Revision | Surface Areas and Volume of SolidsSmart Revision | Surface Areas and Volume of Solids31 mins
Surface Area and Volume of Right Circular CylindersSurface Area and Volume of Right Circular CylindersSurface Area and Volume of Right Circular Cylinders42 mins
Surface Area and Volume of SpheresSurface Area and Volume of SpheresSurface Area and Volume of Spheres40 mins
Quiz | Surface Area and VolumesQuiz | Surface Area and VolumesQuiz | Surface Area and Volumes43 mins
Surface Area and Volume of Right Circular ConeSurface Area and Volume of Right Circular ConeSurface Area and Volume of Right Circular Cone37 mins
R D Sharma | Surface Area and VolumesR D Sharma | Surface Area and VolumesR D Sharma | Surface Area and Volumes39 mins
RD Sharma | Surface areas and volumes of Cube & CuboidRD Sharma | Surface areas and volumes of Cube & CuboidRD Sharma | Surface areas and volumes of Cube & Cuboid33 mins
Quiz | MensurationQuiz | MensurationQuiz | Mensuration42 mins
NCERT | Miscellaneous ShapesNCERT | Miscellaneous ShapesNCERT | Miscellaneous Shapes43 mins
Surface Area and Volume of ConeSurface Area and Volume of ConeSurface Area and Volume of Cone24 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :