Three cubes of metal with edges 3 cm, 4 cm and 5 cm are melted to form a single cube. What is the ratio of the total surface areas of the smaller cubes and the bigger cube.
Answers
@
Hey mate ,
Volume of cube = a^3
Thus ,
Total volume = 3^3 + 4^3 + 5^3
= 27+64+125
= 216 cm^3
Since , this is melted to cast another cube hence the volume remains the same
A^3 = 216
A = 3√216 [ Here 3√ represents cube root ]
A= 6 cm
Thus , Surface area of cube = 6a^2
Thus ,
= 6×3^2
= 6×9
= 54 cm^2
= 6 × 4^2
= 6× 16
= 96 cm^2
= 6× 5^2
= 6× 25
= 150 cm^2
Thus , Total surface area if combined = 54+96+150
= 300 cm^2
Total surface area of bigger cube = 6×6^2
= 6^3
= 216 cm^2
Ratio of smaller to bigger = 300/216
= 25/18
= 25:18
Hope you find it helpful !!!!
Do mark it as brainliest!!!
{ hey mate , since you have not cleared that ratio is needed to be combined of smaller or individual .I have showed combined .if it is for individual then just took the ratio of each individual cube's surface area to bigger cube }
