Question

"Question 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. (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?

Class 9 - Math - Surface Areas and Volumes Page 213"

Answer 1

Lateral surface area of cubical box of edge 10cm = 4×102 cm2 = 400 cm2

Lateral surface area of cuboid box = 2(l+b)×h   = 2×(12.5+10)×8
= 360 cm2

Thus, lateral surface area of the cubical box is greater by (400 – 360) cm2 = 40cm2

2)Total surface area of cubical box of edge 10 cm =6×102cm2=600cm2

Total surface area of cuboidal box = 2(lb + bh + lh)

= 2(12.5×10 + 10×8 + 8×12.5)
 = 610 cm2

Thus, total surface area of cubical box is smaller by 10 cm2

Answer 2

Hey!

here is ur answer .

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(1) Long of Cubical box eadge each ( a ) = 10 cm

.°. Lateral surface area of the cubical box = 4a² = 4 ( 10 )² = 400

Long of Cuboidal box = 12.5 cm

wide = 10 cm

high = 8 cm

.°. Lateral surface area of the cuboidal box = 2 ( l + b ) h

= 2 ( 12.5 + 10 ) ( 8 )

= 360 cm²

.°. Lateral surface area of the cubical box is greater by ( 400 - 360 )cm²

= 40 cm²

(ii ) Total surface area of cubical box = 6a²

= 6 ( 10 )²

= 600 cm²

Total surface area of the cuboidal box = 2lb × 2bh × 2hl

= 2 ( lb × bh × hl )

= 2 [ ( 12.5 ) ( 10 ) + ( 10 ). ( 8 ) + ( 8 ) . ( 12.5 )

= 2 [ 125 + 80 + 100 ]

= 610 cm²

.°. Total surface area of cubical box is smaller by ( 610 - 600 ) cm²

= 10 cm²

hopes I helped

thanks

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