Question

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

i. Which box has a smaller total surface area? 

ii. If each edge of the cube is doubled, how many times will its T.S.A increase?

Answer 1

T.S.A of cube 61²= 6 × 10² = 6 ×100 = 600 cm² 

T.S.A of a cuboid 61² = 6 × 102 = 6 x 100 = 600 cm² 

T.S.A of a cuboid = 2(lb + bh + Ih) 

= 2[12.5 x 10 +10 x 8 + 8 x 12.5] 

= 2[125 + 80 + 100] = 2[305] 

t = 610 cm²

i. The cubical box has smaller total surface area. 

ii. If the side of the cube is doubled its side will be 20cm. 

T.S.A 6l² = 6 × 202 = 6 × 400 = 2400 cm² 

original area = 600cm² 

\(\frac{2400}{600}\) = 4 

∴ Its area will increase by 4 times