Question

cont
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. Cusco
6) Which box has the greater lateral surface area and by how much?
(1Which box has the smaller total surface area and by how much?​

Answer 1

Given -

• Edge of cubical box = 10m

• Dimensions of cuboid box = 12.5m × 10m × 8m

To find -

• Which box have greater L.S.A and smaller T.S.A

Solution -

Let's take cubical box first -

Curved surface area = 4a²

where,

4 = no. of faces

a = sides

on substituting the values -

LSA = 4a²

LSA = 4(10)²

LSA = 4(100)

$\longmapsto$ LSA = 400m³

Now,

Total surface area = 6a²

where,

6 = no. of faces including top and base

a = sides

On substituting the values -

TSA = 6a²

TSA = 6(10)²

TSA = 6(100)

$\longmapsto$ TSA = 600m³

$\therefore$ LSA of cube is 400m³ and TSA = 600m³

Similarly -

Let's take Cuboidal box -

Lateral surface area = 2h(l + b)

where,

h = Height

b = Breadth

l = Length

On substituting the values -

LSA = 2h(l + b)

LSA = 2 × 12.5m (10 + 8)m

LSA = 25m(18)m

$\longmapsto$ LSA = 450m³

Now,

Total surface area = 2(lb + bh + hl)

where,

h = Height

b = Breadth

l = Length

On substituting the values -

TSA = 2(lb + bh + hl)

TSA = 2(10 × 8) + (8 × 12.5) + (12.5 × 10)m

TSA = 2(80) + (100) + (125)m

TSA = 2(305)m

$\longmapsto$ TSA = 610m³

$\therefore$ LSA and TSA of cuboidal box is 450m³ and 610m³

Conclusion -

1. Cuboidal box has greater lateral surface area by 50m³

2. Cubical box has smaller total surface area by 10m³

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Answer 2

Answer:

Given :-

• Edge of cube = 10 cm
• Dimensions of cuboid box = 12.5m × 10m × 8m

To Find :-

• Which box have greater L.S.A and smaller T.S.A

Solution :-

Firstly let's find LSA of cube

$\huge \bf \: LSA = {4a}^{2}$

$\sf \: LSA = 4(10) {}^{2}$

$\sf \: LSA = 4 \times 100$

$\sf \: LSA = 400 \: cm {}^{2}$

Now,

Let's find LSA of Cuboid

$\huge \bf \: LSA = 2h(l + b)$

$\sf LSA = 2(12.5) ( 10 + 8)$

$\sf \:LSA = 25 \times 18$

$\sf \: LSA \: = 450 cm$

Hence Cuboid has greater LSA.

___________________________

$\huge \bf \: TSA = 6 {a}^{2}$

$\sf \: TSA = 6(10) {}^{2}$

$\sf \: TSA = 6 \times 100$

$\sf \: TSA = 600 \: cm$

Now,

Let's find TSA of cuboid

$\huge \bf \: TSA = 2(lb + bh + hl)$

$\sf \: TSA = 2(10 × 8) + (8 × 12.5) + (12.5 × 10)m$

$\sf TSA = 2(80) + (100) + (125)cm$

$\sf TSA = 2(305)cm$

$\sf \: TSA = 610 \: cm$

Hence,

Cubical box has smaller total surface area by 10m³