Question

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

Answer 1

Answer:

SOLUTION :

Given:

Radius of 1st cylinder = 15cm

Height of 1st cylinder = 40 cm

Radius of 2nd cylinder = 20 cm

Height of 2nd cylinder = 45 cm

Also, height of new cylinder = 30 cm

Step-by-step explanation:

ExPlanation:

Let the radius of new cylinder ber cm.

Sum of volumes of 1st and 2nd cylinder = volume of new cylinder

TT x 152x 40 + x 202x 45 = r?x 30

→(225 x 40 + 400 x 45) = r? x 30

» 9000 + 18000 = r? x 30

→ 27000 = r? x 30

r2 = 900

r2? = 302

r = 30 cm

Answer 2

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Given,

Radius of one cylinder (r1) = 15 cm

And height (h1) = 40 cm

Radius of second cylinder (r2) = 20 cm

And height (h2) = 45 cm

Now,

Volume of first cylinder = πr12h1

= 22/7 x 15 x 15 x 40 cm³

= 198000/7 cm³

And,

Volume of second cylinder = πr22h2

= 22/7 x 20 x 20 x 45

= 396000/7 cm³

So, total volume = (198000/7 + 396000/7) cm³

= 594000/7 cm³

Now,

Volume of third cylinder = 594000/7 cm³

And height = 30 cm

Thus,

Radius = ³√(594000/7×7/22×1/30)

= √900 = 30 cm

∴ Radius of the third cylinder = 30 cm

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