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CAT 2004 — QA Question 33

Basics of Mensuration/PrismEasy
Passage / Data

Answer the following question based on the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be _______.

Answer & solution

  • equal to the side of the cube

  • B

    3 times the side of the cube

  • C

    13 times the side of the cube

  • D

    impossible to find from the given information

Solution

Let the side of the cube be a units.

DF, AG and CE are body diagonals each of length a√3 units.

∴ Circumradius of the equilateral triangle = a33 = a units

∴ Circumradius = side of cube

Hence, option (a).

CAT 2004 QA Q33: If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sid — Solution | TheCATExam