Question

A cubical box has each edge 10 cm and another cuboidal box is 13 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?

Answer 1

$\huge \bf \color{green} \mathfrak{Question : - }$

A cubical box has each edge 10 cm and another cuboidal box is 13 cm long, 10 cm wide and 8 cm high.

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

$\huge \bf \color{blue} \mathfrak{Solution : - }$

Side of Cube = 10cm •••(Given)

LSA of Cube = 4 × (Side)²

→ LSA of Cube = 4 × (10cm)²

→ LSA of Cube = 4 × 100cm²

→ LSA of Cube = 400cm²

Length of Cuboid = 13cm •••(Given)

Breadth of Cuboid = 10cm •••(Given)

Height of Cuboid = 8cm •••(Given)

LSA of Cuboid

= 2 × (Length + Breadth) × Height

→ LSA of Cuboid

= 2 × (13cm + 10cm) × 8cm

→ LSA of Cuboid = 2 × 23cm × 8cm

→ LSA of Cuboid = 368cm²

So,

The LSA of Cube is Greater than The LSA of Cuboid by 32cm² (400cm² - 368cm² = 32cm²)

TSA of Cube = 6 × (Side)²

→ TSA of Cube = 6 × (10cm)²

→ TSA of Cube = 6 × 100cm²

→ TSA of Cube = 600cm²

TSA of Cuboid = 2 × (Length × Breadth + Breadth × Height + Height × Breadth)

→ TSA of Cuboid

= 2 × (13cm × 10cm + 10cm × 8cm + 8cm × 13cm)

→ TSA of Cuboid

= 2 × (130cm² + 80cm² + 104cm²)

→ TSA of Cuboid = 2 × (314cm²)

→ TSA of Cuboid = 628cm²

So,

The TSA of Cube is Smaller than The TSA of Cuboid by 28cm² (628cm² - 600cm² = 28cm²)

$\huge \bf \color{orange} \mathfrak{Answer : - }$

1. The LSA of Cube is Greater than The LSA of Cuboid by 32cm²
2. The TSA of Cube is Smaller than The TSA of Cuboid by 28cm²

Answer 2

Given:-

• edge of cubical box = 10cm.
• lenght of another cuboidal box = 13cm.
• width = 10cm
• height = 8cm.

To find:-

• (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?

Solution:-

(i) Lateral surface area of cube = 4edge²

• => 4(10)²

• => 400

lateral surface area of cuboid = 2h(l+b)

• => 2 × 8(13+10)
• => 2 × 184
• => 368

So, the lateral surface area of the cube is larger by (400 −368 = 32)cm²

(ii) Total surface area of cube = 6edge²

• => 6(10)²

• => 600

lateral surface area of cuboid = 2(lb+bh+hl)

• => 2(12.5×10 + 10×8 + 8×12.5)
• => 2(125+80+100)
• => 610

So, the total surface area of cuboid is larger by (610−600=10) cm².

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