Question

Q.1: 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?​

Answer 1

ANSWER
(i) Lateral surface area of cube = 4edge
2

=4(10)
2

=400
​

lateral surface area of cuboid =2h(l+b)
2×8(12.5+10)
=16×22.5
=360
​

So, the lateral surface area of the cube is larger by (400−360=40)cm
2


(ii) Total surface area of cube = 6edge
2

=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) cm

Answer 2

Question :-

1: A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.

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 :-

• edge of cubical box= 10 cm.

Lateral surface area

⠀⠀ = ${4a}^{2}$ = $4×$${10}^{2}$${cm}^{2}$

⠀⠀= 400${cm}^{2}$

Total surface area

⠀⠀= ${6a}^{2}$ = $6×$${10}^{2}$${cm}^{2}$

⠀⠀= 600 ${cm}^{2}$

_____________

Dimensions of cuboidal box :-

• 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[(12.5x10)+ (10x8)+ (8x12.5)]${cm}^{2}$

⠀⠀⠀= 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 ${cm}^{2}$