CAT Practice : Mensuration

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The cross section of a sphere and the area of the newly formed circles.

Cross section of a sphere

    Q.17: A spherical rubber ball of radius 14 cm is cut by a knife at a distance of “x” cm from its centre, into 2 different pieces. What should be the value of “x” such that the cumulative surface area of the newly formed pieces is 3/28 more than the rubber ball’s original surface area?
    1. 11.4 cm
    2. 3 cm
    3. 12.4 cm
    4. 7.5 cm


  • Correct Answer
    Choice C. 12.4 cm.

Detailed Solution

Area  of the ball = 4πr2
= 4π * 14 * 14
= 784π

Cumulative area of the 2 pieces = 3/28 more than the ball's surface area.
Therefore, extra area = 3/28 * 784π = 84π

Now this extra area =  areas of 2 new circles of those 2 pieces
Let area of each new circle = πr12
πr12 = 84π / 2 = 42π
Or r12 = 42

Now, r1, x and r form a right angled triangle.
r2 = x2 + r12
Or x2 = 14*14 - 42
= 196 – 42 = 154
Or x = 12.4 cm

Choice (C) is therefore, the correct answer.

Correct Answer: 12.4 cm.

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More questions from Mensuration

  1. Cone and Frustum
  2. Spheres
  3. Circles and Chords
Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.