a cuboid of dimensions 10 cm 2CM 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
Answers
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.
ow 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.
Area of the cuboid = lbh
= 10 x 2 x 2
= 40 cm³
Since it is divided into 5 cubes ,
Area of one cube = 40/5
= 8 cm³
a³ = 8
a = 2 cm
Ratio = SA of cuboid/SA of cube
= 2(lb +bh +lh)/ 6a²
= 2(10 x 2 + 2 x 2 + 20 x 2) / 6(2)²
= 2(20 + 4 +20) / 6 x 4
= 2 x 44 / 6 x 4
= 88 / 24
= 22 / 6
= 11 / 3
The ratio is 11 : 3