Question

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

given
        edge of cube = 10 cm
        length of cuboid = 12.5 cm 
        breadth of cuboid = 10 cm  
       height  of cuboid = 8 cm
  STEP 1
         LATERAL SURFACE AREA OF CUBE = 4 $(edge)^{2}$
                                                                       = 4 * 10 * 10
                                                                       = 4 * 100
                                                                       = $400 cm^{2}$
  STEP 2
         LATERAL SURFACE AREA OF A CUBOID = 2h (l+ b)
                                                                               = 2 * (lh + bh)
                                                                               = 2 *(12.5 * 8 + 10 * 8)
                                                                               = 2 * (100 + 80)
                                                                               = 2 * 180
                                                                               = $360 cm^{2}$

from the above clearly, we can know that  the cube has more lateral surface area and cuboid has less lateral surface area by 40 $cm^{2}$.

STEP 3
        T.S.A OF CUBE = 6$(edges)^{2}$
                                   = 6 * 10 * 10
                                   =600$cm^{2}$
  STEP 4 
         T.S.A OF CUBOID = 2 (lh +bh+lb)
                                        = 2 (12.5 * 8 + 8 * 10 +12.5 * 10)
                                        = 610 $cm^{2}$
   
 from the above we can clearly understand that  T.S.A of cube is less by 10$cm^{2}$
                                                                                  

Answer 2

Question :-

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 :-

⇒ For the cubical box with edge (a) = 10 cm

Lateral surface area = 4a^2 = 4 x 102 cm^2

= 400 cm^2

Total surface area = 6a^2 = 6 x 102 cm^2

= 600 cm^2

For the cuboidal box with dimensions,

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[(12.5 x 10) + (10 x 8) + (8 x 12.5)] 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.

Plz mrk as brainliest ❤