Question

A cubical box is 15 cm long and another cuboidal box is 25 cm long, 20 cm wide and 10 cm high.
(1) Which box has the smaller lateral area and by how much ?
(2) Which box has the greater total surface area and by how much ?

Answer 1

Answer:

the volume of the cubical box is

=15^3. cm^3=3375 cm^3

the volume of the cuboidal box

=25×20×10cm^3=5000cm^3

total area of the cube is=6(15)^2 cm ^2

=1350 cm^2

total area of the cuboidal box

=2(25×20+20×10+10×25) cm^2

=950cm^2

Answer 2

Step-by-step explanation:

Lateral surface area of Cube =

$4 {a}^{2} \: {cm}^{2}$

a = side of cube

Lateral surface area of cuboid

$= 2 \: lh + 2bh \\ \\ = 2h(l + b) \: {cm}^{2}$

Here l = length

b = breadth

h = height

(1) Which box has the smaller lateral area and by how much ?

ATQ

A cubical box is 15 cm long,i.e.

a = 15 cm

lateral surface area of cube

$= 4 \times {(15)}^{2} \\ \\ = 4 \times 225 \\ \\ = 900 \: {cm}^{2}$

The dimension of cuboid l = 25 cm

b= 20 cm

h = 10

Lateral surface area of cuboid

$= 2 \times 10(25 + 20) \\ \\ = 20 \times 45 \\ \\ = 900 {cm}^{2}$

Lateral surface area of both boxes are equal.

(2) Which box has the greater total surface area and by how much ?

TSA of cube

$= 6 {a}^{2} \\ \\ = 6 \times 225 \\ \\ = 1350 \: {cm}^{2}$

TSA of cuboid

$= 2(lb + bh + hl) \\ \\ = 2(25 \times 20 + 20 \times 10 + 25 \times 10) \\ \\ = 2(500 + 200 + 250) \\ \\ = 2 \times 950 \\ \\ = 1900 \: {cm}^{2}$

So Total surface area of cuboidal box is more.

How much more =1900-1350

= 550 sq-cm

Hope it helps you.