Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the
surface area of the new cube.
(1) 210 cm2
(1) 213 cm2
(3) 224 cm2
(4) 216 cm2
Answers
Answer:
(4) 216 cm2
Step-by-step explanation:
Edge of 1st cube = 3cm
Volume of 1st cube = edge^3
=3^3
=27cm^3
Edge of 2nd cube=4cm
Volume of 2nd cube =4^3
=64cm^3
Edge of 3rd cube =5cm
Volume of 3rd cube =5^3
=125cm^3
Total volume of the 3 cubes =Volume of new cube
Volume of new cube = 27 +64+125cm^3
=216cm^3
Edge^3=216
Edge=6cm
Surface area of the new cube = 6×edge^2
=6×6^2
=216cm^2
Formula used: 1. volume of any cube = a*a*a or ( a^3).
2. surface area of a cube= 6*a*a , where a =side of cube .
Concept:
Since the three cubes are melted to form a new single cube,
the volume of the new cube=(sum of volumes of the cubes).
Working:
Now,sum of volumes of cubes=(3*3*3)+(4*4*4)+(5*5*5)=216 cm3
so, volume of new single cube=216
=> a^3=216
=>a=cube root of(216)
=>a=6 cm , where a= side of the single cube.
Surface area of the new cube= 6*(6^2)
=6*6*6
=216 cm2