Question

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5. A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long. 10 cm
wide and 8 cm high
(i) Which box has the greater lateral surface area and by how much?
00) Which box has the smaller total surface area and by how much?​

Answer 1

solution :-

Edge of the cube = 10cm

Lateral surface area of cube = 4a²

=> 4(10)²

=> 4 × 100

=> 400 cm²

Total surface area of cube = 6a²

=> 6(10)²

=> 6 × 100

=> 600 cm²

Dimension of cuboid

Length = 12.5cm

breadth = 10cm

height = 8cm

Lateral surface area of cuboid = 2h ( L + b)

=> 2×8(12.5 + 10)

=> 16 × 22.5

=> 360 cm²

Total surface area of cuboid = 2( Lb + Bh + Lh)

=> 2(12.5× 10 + 10×8 +12.5×8)

=> 2(125 + 80 + 100)

=> 2 ×305

=> 610 cm²

I) Which box has the greater lateral surface area and by how much?

LSA of cube = $\sf {400cm}^{2}$

LSA of cuboid = $\sf{360cm}^{2}$

= 400 - 360

=$\sf{40cm}^{2}$

Cube has the greater lateral surface area by $\sf{40cm}^{2}.$

II) Which box has the smaller total surface area by how much?

TSA of cube =$\sf{600cm}^{2}$

TSA of cuboid = $\sf{610cm}^{2}$

$\sf= 610 - 600 = {10cm}^{2}$

Cube has the smaller total surface area by $\sf{10cm}^{2}$

Answer 2

Question :-

5. A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long. 10 cm

wide and 8 cm high

(i) Which box has the greater lateral surface area and by how much?

00) Which box has the smaller total surface area and by how much?

Answer :-

• edge of cubical box (a) = 10 cm
• Lateral surface area = 4${a}^{2}$

⠀= 4 x 102 ${cm}^{2}$

⠀= 400 ${cm}^{2}$

Total surface area = 6${a}^{2}$

⠀= 6 x 102${cm}^{2}$

⠀= 600${cm}^{2}$

_________

For the cuboidal box with dimensions,

• Length (l) = 12.5 cm,
• Breadth (b) = 10 cm,
• Height (h) = 8 cm

∴ Lateral surface area

⠀⠀= 2[l + b] x h

⠀⠀= 2[12.5 + 10] x 8 ${cm}^{2}$

⠀⠀ = 360 ${cm}^{2}$

Total surface area

⠀⠀ = 2[lb + bh + hl]

⠀⠀= 2[(12.5 x 10) + (10 x 8) + (8 x 12.5)] ${cm}^{2}$

⠀⠀= 2[125 + 80 + 100] ${cm}^{2}$

⠀⠀= 2[305] ${cm}^{2}$

⠀⠀= 610 ${cm}^{2}$

__________

A cubical box has the greater lateral surface area by

(400 – 360) ${cm}^{2}$

= 40 ${cm}^{2}$

(ii) Total surface area of a cubical box is smaller than the cuboidal box by

(610 – 600) ${cm}^{2}$

= 10 ${cm}^{2}$