Question

a cuboid of dimensions 10 cm by 2 cm by 2 m is divided into 5 cubes of H2 cm find the ratio of the total surface area of the cuboid and that of the cubes

Answer 1

Given length of a cuboid = 10cm.

Given Breadth of a cuboid = 2cm.

Given Height of a cuboid = 2cm.

We know that volume of a cuboid = l * b * h

                                                         = 10 * 2 * 2

                                                          = 40 cm^3.

We know that Total surface area of a cuboid = 2(lb + bh + hl)

                                                                           = 2(10 * 2 + 2 * 2 + 2 * 10)

                                                                           = 2(20 + 4 + 20)

                                                                           = 88cm^2.


Given that it is divided into 5 cubes of edge 2cm.

We know that total surface of 1 cube = 6s^2 = 6 * 2 * 2 = 24 cm.

Then the total surface area of 5 cubes =  24 * 5 = 120 cm.

Therefore the ratio of the TSA of the cuboid/TSA of cubes

= 88 : 120

= 11:15.
hope this helps

Answer 2

Given length of a cuboid = 10cm.

Given Breadth of a cuboid = 2cm.

Given Height of a cuboid = 2cm.

We know that volume of a cuboid = l * b * h

                                                         = 10 * 2 * 2

                                                          = 40 cm^3.

We know that Total surface area of a cuboid = 2(lb + bh + hl)

                                                                           = 2(10 * 2 + 2 * 2 + 2 * 10)

                                                                           = 2(20 + 4 + 20)

                                                                           = 88cm^2.


Given that it is divided into 5 cubes of edge 2cm.

We know that total surface of 1 cube = 6s^2 = 6 * 2 * 2 = 24 cm.

Then the total surface area of 5 cubes =  24 * 5 = 120 cm.

Therefore the ratio of the TSA of the cuboid/TSA of cubes

= 88 : 120

= 11:15.


Hope this helps!