Mensuration Practice Test 9

Question : 25 of 40

Marks: +1, -0

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. The fraction of water that overflows is:

Validate

Solution:

(BC)^2

6^2+8^2

BC =

√{36+64}

BC = 10 cm
AB = BD = 6 cm

So, CD = 10 − 6 = 4 cm
OC = 8 - r

OC^2

OD^2 + CD^2

(8-r)^2

r^2+(4)^2

64 +

r^2

- 16r =

r^2+16

48 = 16r
⇒ r = 3 cm
Fraction of water that overflows
=

{\Volume \od \the \spheres}/{\Volume \of \the \cone}

{4/3 π(r)^3}/{1/3π(R)^2H}

{4(3)^3}/{(6)^2×8}

3/8

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