Question

The content of 3 cylinders each of radius 2 cm and height 1 cm is to be poured into a cone of

height 9 cm. What is the radius of the cone?

Answer 1

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Answer 2

The correct answer is $\frac{2}{3}$ cm.

Given: Radius of small cylinder = 2 cm.

Height of small cylinder = 1 cm.

Height of big cylinder = 9 cm.

To Find: Radius of big cylinder.

Solution:

As same amount of liquid is poured, the volume of bigger cylinder and all the three cylinders will be same.

Sum of volume of all three cylinders = Volume of big cylinder

Volume = $\pi r^{2} h$

Volume of small cylinder = $\pi (2)^{2} (1)$ = $4\pi$

Volume of 3 small cylinders = 3(volume of 1 cylinder) = 3($4\pi$) = $12\pi$

Let the radius of big cylinder = r

Volume of big cylinder = $\pi (r)^{2} (9)$ = $9\pi r^{2}$

Now equate the volumes.

$4\pi =9\pi r^{2}$

$r^{2} =\frac{4}{9}$

r = $\frac{2}{3}$

Hence, the radius of big cylinder is $\frac{2}{3}$ cm.

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