NCERT Class 9 Solutions: Surface Areas and Volumes (Chapter 13) Exercise 13.1 – Part 2

Q-4 The paint in a certain container is sufficient to paint an area equal to 9.375m2 . How many bricks of dimensions 22.5cm×10cm×7.5cm can be painted out of this container?

Box: Rectangular Prism with surface area A=2(wh+lw+lh)

Box: Rectangular Prism

Box: Rectangular Prism with surface area A=2(wh+lw+lh)

Solution:

  • The container can paint an area =9.375m2=93750cm2

  • Dimensions of brick =22.5cm×10cm×7.5cm

Therefore, total surface area of a brick

  • 2(lb+bh+lh)cm2

  • 2(22.5×10+10×7.5+22.5×7.5)cm2

  • 2(225+75+168.75)cm2

  • 2×468.75cm2=937.5cm2

Number of bricks can be painted TotalareathatcanbepaintedTotalsurfaceareaofabrick = 93750937.5=100

Q-5 A cubical box has each edge 10cm and another cuboidal box is 12.5cm long, 10cm wide and 8cm high.

  1. Which box has the greater lateral surface area and by how much?

  2. Which box has the smaller total surface area and by how much?

Solution:

Surface area of cuboid is 2(lw+hw+lh)

Surface Area of Cuboid

Surface area of cuboid is 2(lw+hw+lh)

  • Cubical box has each edge 10cm

  • Length l=12.5cm

  • Width b=10cm

  • Height h=8cm

Lateral surface area is the area of the faces along the height. That is, it is the area excluding the top and bottom. Now for cube this would be the area of any 4 faces. For the cuboid it would be 2(l×h)+2(b×h)

Solution (i)

  • Lateral surface area of cubical box of edge 10cm=4×102cm2=400cm2

  • Lateral surface area of cuboid box is 2(l+b)×h=2×(12.5+10)×8cm2=2×22.5×8cm2=360cm2

  • Thus, lateral surface area of the cubical box is greater by (400360)cm2=40cm2

Total surface area of cubical box of edge 10cm=6×102cm2=600cm2

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

= 2(12.5×10+10×8+8×12.5)cm2

= 2(125+80+100)cm2

= (2×305)cm2=610cm2

So, total surface area of cubical box is smaller by (610600)cm2=10cm2

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