Question

A cubical box has each edge 12 cm and another cuboidal box is 15 cm long, 10 cm wide and 9 cm high.
(a) Which box has the greater lateral surface area and by how much?
(b) Which box has the smaller volume and by how much?​

Answer 1

(a) answer - A cuboid has six faces and the total surface area is the sum of the surface area of the 6 faces and the Lateral surface area is the sum of the area of the four faces. Thus, the cubical box has a greater lateral surface area by 40 cm2 and the cubical box has a smaller total surface area by 10 cm2.

(b) 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

2