Question

two Cylinderical vessels are filled with oil. the radius of one vessel is 15 and it's height is 25 cm. the radius and height of another vessel is 10 cm and 18 cm respectively. find radius of the Cylinderical vessels 30 cm in height which will just contain the oil of the two given vessels.​

Answer 1

Answer:

$\bigstar{\bold{Radius=15.7\:cm}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Radius of first vessel (r₁) = 15 cm
• Height of first vessel (h1) = 25 cm
• Radius of second vessel (r₂) = 10 cm
• Height of second vessel (h₂) = 18 cm
• Height of third vessel (H) = 30 cm

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Radius of third vessel (R)

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ First we have to find the volume of the first two vessels.

→ The volume of a cylinder is given by,

  Volume of a cylinder = π r² h

→ Finding the volume of the first vessel by substituting the datas,

  Volume of first vessel = 3.14 × 15 × 15 ×25

  Volume of first vessel = 47.1 × 375

  Volume of first vessel = 17662.5 cm³

→ The volume of the second vessel is given by

   Volume of the second vessel = 3.14 × 10 × 10 × 18

   Volume of the second vessel = 31.4 × 180

   Volume of the second vessel = 5652 cm³

→ By given we know that,

  Volume of third vessel = Volume of first vessel + Volume of second vessel

→ Hence

  Volume of third vessel = 17662.5 + 5652

  Volume of third vessel = 23314.5 cm³

→ But we know that

  π R² H = 23314.5

→ Substituting the value of H

  3.14 × R² × 30 = 23314.5

  94.2 R² = 23314.5

  R² = 23314.5/94.2

  R² = 247.5

  R = √247.5

  R = 15.7 cm

→ Hence radius of the vessel is 15.7 cm

$\boxed{\bold{Radius=15.7\:cm}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ Volume of a cylinder is given by the formula,

   Volume of a cylinder = π r² h