NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.1 – Part 3

different types of shape and its volume,area of surface,total area

Different Types of Shape

different types of shape and its volume,area of surface,total area

Q-6 A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25cm wide and 25cm high.

  1. What is the area of the glass?

  2. How much of tape is needed for all the 12edges ?

Solution:

Faces, Vertex and Edges of a Cuboid

Edges in a Cuboid

Faces, Vertex and Edges of a Cuboid

Solution (i)

Dimensions of greenhouse are l=30cm,b=25cm,h=25cm

Total surface area of greenhouse are the areas of its 6 faces (3 faces each appear twice on opposite sides) = 2(lb+bh+lh)

  • =2(30×25+25×25+25×30)cm2

  • =2(750+625+750)cm2

  • =4250cm2

Solution (ii)

Length of the tape needed is the length of all its edges. Note that all the edge lengths appear 4 times (2 times on opposite sides of each face with a similar face appearing on opposite side of a the cube). Therefor the total length of all the edges = 4(l+b+h)

  • =4(30+25+25)cm

  • =4×80cm

  • =320cm

Q-7 Shanti Sweets Stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions 25cm×20cm×5cm and the smaller of dimensions 1 5cm×12cm×5cm . For all the overlaps, 5% of the total surface area is required extra. If the cost of the cardboard is Rs. 4for1000cm2 , find the cost of cardboard required for supplying 250 boxes of each kind.

Solution:

Dimension of bigger box =25cm×20cm×5cm . Therefore, total surface area of 1 bigger box (area of all the faces) = 2(lb+bh+lh)

  • = 2(25×20+20×5+25×5)cm2

  • = 2(500+100+125)cm2

  • = 2(725)

  • = 1450cm2

Dimension of smaller box =15cm×12cm×5cm , therefore, total surface area of smaller box = 2(lb+bh+lh)

  • = 2(15×12+12×5+15×5)cm2

  • = 2(180+60+75)cm2

  • = 2(315)

  • = 630cm2

Therefore total surface area of 250 boxes of each type 250(1450+630)cm2 = 250×2080cm2=520000cm2

The overlaps require 5% extra area, therefore extra area required =5100(1450+630)×250cm2=26000cm2

Total Cardboard required =520000+26000cm2=546000cm2

One cardboard sheet has area 1000cm2 . Therefore the number of sheets required = 5460001000=546 . Cost of 1 sheet is 4 Rs. Therefore, total cost of 546 cardboard sheet 4×546=Rs.2184

Q-8 Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4m × 3m?Solution:

There is no top, so tarpaulin is only required for the four sides and top. Therefore, Tarpaulin required = 2l×h+b×h+lb = 2(l+b)×h+lb = [2(4+3)×2.5+4×3]m2 = (35+12)m2 = 47m2

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