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?
3.if each edge of the cube is doubled, how times will its total surface area increase?

Answer 1

$<b><font color ="red"> ( i ) In a cube side= 10cm lateral surface area of cube =4*side^2 4*10^2=400 cm^2 In a cuboid length =12.5 CM breadth =10 CM height =8 cm lateral surface area of cuboid =2*(l+b)*h 2*(12.5+10)*8 =360 CM ^2 cube box have larger area difference =400-360= 40 cm^2$

$<b><font color =" purple "> (ii) In a cube total surface area of cube =6*side^2 6*10^2=600cm ^2 In a cuboid total surface area of cuboid =2*(lb+bh+hl) 2*(12.5*10+10*8+8*12.5) 2*(125+80+100) =610cm ^2 cube have smaller total surface area difference =610-600=10cm^2$

$<b><font color ="blue" > (iii) cube side =2* side=2*10=20 cm total surface area of cube =6*side^2 6*20^2=6*400=2400cm ^2 intial t. s. a. =600cm^2present t. s.a=2400cm^2 difference =2400-600=1800cm^2$