CAT Practice : Mensuration

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Cutting a sphere into two equal parts increases its surface area by 50%, what will be the increase if we cut it in some other fashion?


    Q.2: A sphere of radius r is cut by a plane at a distance of h from its center, thereby breaking this sphere into two different pieces. The cumulative surface area of these two pieces is 25% more than that of the sphere. Find h.


  • Correct Answer
    Choice A.

Explanatory Answer

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Detailed Solution

Area = 4πr2

Cumulative area of the two pieces = 25% more than the by square.
Area of 2 pieces = 1.25 × 4π2 = 5πr2
Extra area = πr2
Extra area = area of two new circles that are now created circles.
Area each new circle =

Let radius of new circle be r1.
Now, πr12 =
r1 =

Now, r1, h and r form a right angled triangle.
h2 + r12 = r2
h2 + = r2
h =
Answer choice (A)

Correct Answer:

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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.