Question

cuboidal box is to as 12.5 CM Long. 10cm
and 8 CM high.
1 which box has the greater lateral surface
and by how much?

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

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Answer 1

Answer:

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cmwide and 8 cm high. (i) Which box has the greater lateral surface area and by how much?(ii) Which box has the smaller total surface area and by how much? difference=600-592=8cm2.

Step-by-step explanation:

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Answer 2

Question ::-

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?

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

Given ::-

• Length of cuboid = 12.5cm

• Height of cuboid = 8cm

To find ::-

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

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

Solution ::-

For the cubical box with edge

(a) = 10 cm

Lateral surface area

= ${4a}^{2}$

= 4 x ${10}^{2}$ ${cm}^{2}$

= 400 ${cm}^{2}$

_______

Total surface area

= ${6a}^{2}$

= 6 x ${10}^{2}$ ${cm}^{2}$

= 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 ${cm}^{2}$

___________

(i) 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 ${cm}^{2}$