Multiple choice

A square hole of cross - sectional area $4\displaystyle cm^{2}$ is drilled across a cube with its length parallel to a side of the cube. If edge of the cube measures $5 cm$, what is the total surface area of the body so formed?

  1. $140 cm^{2}$
  2. $142 cm^{2}$
  3. $162 cm^{2}$
  4. $182 cm^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of cube = 6 * 5^2 = 150. When a hole is drilled, we lose two faces of area 4, but gain the internal surface area of the hole. Internal area = perimeter * length = 4 * sqrt(4) * 5 = 4 * 2 * 5 = 40. Total = 150 - 2*4 + 40 = 182.

AI explanation

The original surface area of the cube is 6 multiplied by 5 squared, which equals 150 square centimeters. Drilling the hole removes two square faces from the total surface area, reducing it by 8 square centimeters, but it adds the inner lateral surface area of the hole. The lateral surface area is found by multiplying the perimeter of the hole, which is 8 centimeters, by the depth of the cube, which is 5 centimeters, adding 40 square centimeters. The new total surface area is 150 minus 8 plus 40, resulting in 182 square centimeters.

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