Question

A cubical box has each edge 10cm and another cuboidal box is 12.5 cm × 10 cm long , 10 cm wide and 8 cm high
1. which box has the greater lateral surface area and by how much.
2.which box has the smaller total surface area and by how much

Answer 1

(i) LSA of cube = 4(side)^2
= 4( 10×10 )
= 400 sq. cm
LSA of cuboid = 2(l+b)h
= 2(12.5 + 10)8
= 360 sq. cm
Cube has greater LSA by 40 sq. cm.
(ii) TSA of cube = 6(side)^2
= 6(10×10)
= 600 sq. cm
TSA of cuboid = 2(lb+bh+hl)
= 2(12.5×10 + 10×8 + 8×12.5)
= 610 sq. cm
TSA of cube is smaller by 10 sq. cm

Answer 2

★ Given:-

Edge of a cube = 10 cm

Length, l = 12.5 cm

Breadth, b = 10cm

Height, h = 8 cm

★ To find:-

1) The lateral surface area for both the figures.

Lateral surface area of cubical box = 4 (edge)²

= 4(10)²

= 400 cm² → (1)

Lateral surface area of cubodal box = 2[lh + bh]

= [2(12.5 × 8 + 10 × 8)]

= (2 × 180) = 360

Therefore, Lateral surface area of cubodal box is 360 cm² → (2)

★ Point to be remembered:-

From (1) and (2), lateral surface area of the cubical box is more than the lateral surface area of the cubodial box. The difference between both the lateral surfaces is 40 cm².

Lateral surface area of cubical box – Lateral surface area of cubodial box=400cm² – 360cm² = 40 cm²

★ To find:-

2) The total surface area for both the figures

The total surface area of the cubical box = 6 (edge)² = 6 (10 cm)² = 600 cm² → (3)

Total surface area of cuboidal box

= 2[lh + bh + lb]

= [2(12.5 × 8 + 10 × 8 + 12.5 × 100]

= 610

This implies that total surface area of cuboidal box is 610 cm² → (4)

★ Point to be remembered:-

From (3) and (4), the total surface area of the cubical box is smaller than that of the cuboidal box. And their difference is 10cm².

Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 cm²