Question 45
Mensuration of Plane ShapesHow many 2√2cm diameter discs can be cut out of a sheet of cardboard 218√2π¾ cm long and √2π¼cm wide?
- A.49
- B.219
- C.217π¾(√2 + 2)
- D.218π5/4(1 + √2)
- E.49(√2 − 1)
Show the answer and explanation
Answer: A (49)
Explanation
Divide the areas: the sheet is 2¹⁸√2π^¾ × √2π^¼ = 2¹⁹π cm² and each disc is π(√2)² = 2π cm², giving 2¹⁸ = 4⁹ discs.