Math, asked by kumawatson9, 14 days ago

A cubical box has each edge 12 cm and another cuboidal box is 15 cm long, 10 cm wide and 9 cm high.
(a) Which box has the greater lateral surface area and by how much?​

Answers

Answered by jeevanchris9
0

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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