Question

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

➡️Please solve this..​

Answer 1

▫️Given :▫️

Radius of 1st cylinder = 15 cm

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

▪️Explanation ▪️

Let the radius of new cylinder be r cm.

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

=π×(15)^2×40+π×(20)^2×45=πr^2×30

⇒(225×40+400×45)=r^2×30

⇒9000+18000=r^2×30

⇒27000=r^2×30

⇒r^2=900

⇒r^2=(30)^2

⇒r=30 cm.

Hence, the radius is 30 cm.

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

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

ExPlanation:

Let the radius of new cylinder be r cm.

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

π × 152× 40 + π × 202× 45 = πr²× 30

⇒(225 × 40 + 400 × 45) = r² × 30

⇒ 9000 + 18000 = r² × 30

⇒27000 = r² × 30

⇒r² = 900

⇒r² = 302

⇒r = 30 cm

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