Question : A cuboid whose sides are 8 cm, 27 cm, and 64 cm is melted to form a new cube. What is the respective ratio of the total surface area of the cuboid and cube?
Option 1: 307 : 216
Option 2: 291 : 203
Option 3: 349 : 248
Option 4: 329 : 237
Correct Answer: 307 : 216
Solution :
Sides of cuboid = 8 cm, 27 cm, and 64 cm
Let $a$ be the side of the cube.
The volume of the cuboid = volume of the cube
$lbh$ = $a^3$
8 × 27 × 64 = $ a^3$
$a$ = $\sqrt[3]{8 × 27 × 64}$ = 2 × 3 × 4 = 24 cm
Total surface area of cuboid = $2(lb+ bh + hl)$
Total surface area of cuboid = 2 × (8 × 27 + 27 × 64 + 64 × 8)
= 2 × (216 + 1728 + 512)
= 2 × 2456
= 4912
The total surface area of the cube = $6a^2$
= 6 × 24 × 24
= 3456
Required ratio = 4912 : 3456
= 307 : 216
Hence, the correct answer is 307 : 216.
Related Questions
Know More about
Staff Selection Commission Multi Tasking ...
Application | Cutoff | Selection Process | Preparation Tips | Eligibility | Exam Pattern | Admit Card
Get Updates Brochure
Your Staff Selection Commission Multi Tasking Staff Exam brochure has been successfully mailed to your registered email id “”.
