Question

a cuboid of dimension 10 cm by 2 cm by 2 cm is divided into 5 cubes of edge 2 cm. find the ratio of the total surface area of the cuboid and that of the cubes

Answer 1

Answer:

The ratio is 11:15.

Step-by-step explanation:

Given : A cuboid of dimension 10 cm by 2 cm by 2 cm is divided into 5 cubes of edge 2 cm.

To find : The ratio of the total surface area of the cuboid and that of the cubes?

Solution :

Length of a cuboid = 10 cm

Breadth of a cuboid = 2 cm

Height of a cuboid = 2 cm

Volume of a cuboid is

$V=l\times b\times h$

$V=10\times 2\times 2$

$V=40 cm^3$

Total surface area of a cuboid is

$TSA=2(lb + bh + hl)$

$TSA=2(10\times 2 + 2\times 2 +2\times 10)$

$TSA=2(20+4+20)$

$TSA=2(44)$

$TSA=88cm^2$

It is divided into 5 cubes of edge 2cm.

Total surface of 1 cube

$TSA=6s^2\\TSA=6\times 2\times 2\\TSA=24 cm^2$

The total surface area of 5 cubes is $24\times 5=120 cm^2$

The ratio of the TSA of the cuboid and TSA of cubes is

$r=88:120\\r=11:15$

Therefore, The ratio is 11:15.

Answer 2

see the above image....