Question

Two cylindrical vessels are filled with milk. The radius of one vessel is 15 cm and height is 40cm,radius of other vessel is 20cm and height is 45 cm. Find the radius of another cylindrical vessel of height 30cm which may just contain the milk which is in the two given vessels.

Answer 1

Radius of the first vessel (r1) = 15 cm
Height of the first vessel (h1) = 40 cm
Volume of the first vessel = πr1²h1
= 22/7 × 15 × 15 × 40
Volume of the first vessel = 28285.7143 cm³
Radius of the second vessel (r2) = 20 cm
Height of the second vessel (h2) = 45 cm
Volume = 22/7 × 20 × 20 × 45
Volume of the second vessel = 56571.4286 cm³
Now , given that
The height of the third vessel which contain milk of the given two vessels (h) = 30 cm.
Volume of the third vessel = volume of the first vessel + volume of the second vessel.
∴ 22/7 × r² × 30 = (28285.7143 + 56571.4286)
660r² = 84857.1429 × 7
660r² = 594000
r² = 594000/660
r² = 900
r =√900
r = 30 cm
So, the radius of the third vessel is 30 cm, which will contain the milk which is in the two given vessels.