CAT question in mensuration. prepared by rajesh balasubramanian CAT 100%iler in CAT 2011, 2012 and 2014.

1. Mensuration

2. Mensuration
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.
(a)
r
2
(b)
r
3
(c)
r
5
(d)
r
6

3. Mensuration
Area = 4pr2
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.

4. Mensuration
Cumulative area of the two pieces = 25% more than the by square.
Area of 2 pieces = 1.25 × 4p2 = 5pr2
Extra area = pr2
Extra area = area of two new circles that are now created circles.
Area each new circle =
πr2
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.

5. Mensuration
Let radius of new circle be r1.
Now, pr1
2 =
πr2
2
r1 =
r
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.

6. Mensuration
Now, r1, h and r form a right angled triangle.
h2 + r1
2 = r2
h2 +
r
2
2
= r2
h =
r
2
Answer choice (a)
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.

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