Multiple choice

From a cuboidal cardboard box of dimensions $80\;cm\times40\;cm\times15\;cm,\;6$ circles of radius $7\;cm$ were cut out from the front face. Find the surface area of the remaining box.

  1. $9176\;cm^2$
  2. $9066\;cm^2$
  3. $9776\;cm^2$
  4. $9076\;cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of cuboid = 2(lb + bh + lh) = 2(80*40 + 40*15 + 80*15) = 2(3200 + 600 + 1200) = 10000. Area removed = 6 * (pi * r^2) = 6 * (22/7) * 49 = 6 * 22 * 7 = 924. Remaining area = 10000 - 924 = 9076 cm^2.

AI explanation

The total surface area of the closed cuboid is 2*(80*40 + 80*15 + 40*15) = 2*(3200 + 1200 + 600) = 10000 square cm. The area removed from the front face is 6 * pi * 7^2 = 6 * (22/7) * 49 = 924 square cm. Therefore, the surface area of the remaining box is 10000 - 924 = 9076 square cm.

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