CDS 2026 (I) Elementary Mathematics, question 66

Topic: Mensuration

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Q66

A metallic sheet of rectangular shape is 48 cm×36 cm48\text{ cm}\times 36\text{ cm}. From each corner a square of side xx cm is cut off and an open box is made of the remaining sheet. If the box holds 5.125.12 litre of water, then what is the value of xx ?

  1. (a) 66 cm
  2. (b) 7.57.5 cm
  3. (c) 88 cmCorrect answer
  4. (d) 8.58.5 cm

Solution.

Answer: (c) 88 cm

  1. After cutting and folding, the box dimensions are x,48−2xx,48 - 2x and 36−2x36 - 2x cm.
  2. Since 5.12 litres =5120cm3= 5120{cm}^{3}, solve x(48−2x)(36−2x)=5120x(48 - 2x)(36 - 2x) = 5120.
  3. Testing x=8x = 8 gives 8×32×20=51208 \times 32 \times 20 = 5120, so the listed answer is (c).