a cubiod of demensions 10cm×2cm×2cm is divided into cubes of edge 2cm .find the ratio of the total surface area of the cubiod and that of the cubes.
Answers
Step-by-step explanation:
first of all we have to find how many cubes are formed
so
Volume of cuboid=no. of cubes * Volume of a cube
ie
l*b*h= n* a³
10*2*2=n*2³
n=5 cubes
therefore
ratio of Surface areas= Surface area of cuboid/
Surface are of cubes
ratio= 2(lb+lh+bh)/5*6a²
= (10*2+10*2+2*2)/15*2²
=24/60
= 2/5
therefore ratio is 2:5
probably it helps and mark ut as brainliest please
Volume of cuboid - 10×2×2 = 40 cm^3
Volume of cube - 2×2×2 = 8 cm^3
No. of cubes = volume of cuboid / volume of cube
= 40/8 = 5 cubes
Total surface area of cuboid = 2 ( lb + bh + hl )
= 2 ( 20 + 4 + 20 )
= 88 cm^2
Total surface area of 1 cube = 6 × a^2
= 6 × 2 × 2 = 24 cm^2
Total surface area of 5 cubes = 24×5 = 120 cm^2
Ratio of Total Surface area of cuboid to Ratio of Total Surface area of all cubes = 88 : 120 = 11 : 15
Therefore, the answer is 11 : 15