A cuboidal box had length 20cm breadth 10cm and 8.5 respectively and cubical box of edge 13.5 cm find the smaller and the greater lateral surface area and the total surface area, please help me with this (╯°□°）╯︵ ┻━┻
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Answer:
Given: The length of the edge of the cubical box is 10cm and the length, breadth, and height of the cuboidal box are 12.5 cm, 10 cm, and 8 cm respectively.
A cube is a cuboid whose length, breadth, and height and equal. A cuboid has six faces and the total surface area is the sum of the surface area of the 6 faces and the Lateral surface area is the sum of the area of the four faces.
Total surface area of cube = 6a2 (where, 'a' is the side of the cube)
Total surface area of cuboid = 2(lb + bh + hl)
Lateral surface area of a cube = 4a2
Lateral surface area of cuboid = 2(l + b)h
Edge length of the cube, a = 10 cm
Length of the cuboid, l = 12.5 cm
Breadth of the cuboid, b = 10 cm
Height of the cuboid, h = 8 cm
Lateral surface area of the cube = 4a2
= 4 × (10 cm)2
= 4 × 100 cm2
= 400 cm2
Lateral surface area of the cuboid = (l + b)h
= 2 × (12.5 cm + 10 cm) × 8 cm
= 2 × 22.5 cm × 8 cm
= 360 cm2
We see that, the cubical box has a greater lateral surface area by (400 cm2 - 360 cm2) = 40 cm2
Total surface area of the cube = 6a2
= 6 × (10 cm)2
= 6 × 100 cm2
= 600 cm2
Total surface area of the cuboid = 2(lb + bh + hl)
2(lb + bh + hl) = 2 × (12.5 cm × 10 cm + 10 cm × 8 cm + 8 cm × 12.5 cm)
= 2 × (125 cm2 + 80 cm2 + 100 cm2)
= 2 × 305 cm2
= 610 cm2
Cubical box has a smaller total surface area by (610 cm2 - 600 cm2) = 10 cm2
Thus, the cubical box has a greater lateral surface area by 40 cm2 and the cubical box has a smaller total surface area by 10 cm2.
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