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Three cubes of edges 3 cm, 4 cm, and 5 cm are melted and formed into a single cube. What is the percentage change in the total surface area after melt
Question

Three cubes of edges 3 cm, 4 cm, and 5 cm are melted and formed into a single cube. What is the percentage change in the total surface area after melting and recasting?

A.

22% increase

B.

22% decrease

C.

28% increase

D.

28% decrease

Correct option is D

Given:
Edges of three cubes = 3 cm, 4 cm, and 5 cm
Formula Used:
Volume of cube = a3a^3​​
Total surface area = 6a26a^2​​
Solution:
Calculate the total volume of the three cubes:
33+43+533^3 + 4^3 + 5^3​ = 27 + 64 + 125 = 216
Find the edge length of the new single cube:
a3a^3​ = 216
a = 6
Calculate the initial total surface area:
6×(32+42+52)6 × (3^2 + 4^2 + 5^2)​ = 6 × (9 + 16 + 25) = 6 × 50 = 300
Calculate the total surface area of the new cube:
6 × 626^2​ = 6 × 36 = 216
Calculate the decrease in area:
300 - 216 = 84
Calculate the percentage change:
84300\frac{84}{300}​ × 100 = 28
Final Answer
So the correct answer is (d)

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