Multiple choice

Two rectangular solids of same metal with dimensions 2.5 cm, 4 cm, 8 cm and 4 cm, 9 cm, 12 cm are melted to frame a single rectangular solid with length 16 cm and width 4 cm. What is the surface area of this new solid?

  1. 352 sq. cm

  2. 380 sq. cm

  3. 448 sq. cm

  4. 496 sq. cm

  5. 540 sq. cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume 1 = 2.5*4*8 = 80. Volume 2 = 4*9*12 = 432. Total volume = 512. New solid: 16*4*h = 512 => 64h = 512 => h = 8. Surface area = 2(lw + lh + wh) = 2(16*4 + 16*8 + 4*8) = 2(64 + 128 + 32) = 2(224) = 448.

AI explanation

Adding the volumes of the two solids gives a total volume of (2.5 times 4 times 8) plus (4 times 9 times 12), which equals 80 plus 432, or 512 cubic cm. For the new solid, the volume equals length times width times height, so 16 times 4 times height equals 512; solving this gives a height of 8 cm. The total surface area of this cuboid is 2 times (16 times 4 plus 16 times 8 plus 4 times 8), which equals 2 times (64 plus 128 plus 32), resulting in 448 sq cm.

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