Volume Solution2





In this page volume solution2 we are going to see solution of each questions of the worksheet volume worksheet1.

Question 4:

Volume of a solid cylinder is 62.37 cu.cm. Find the radius if its height is 4.5 cm

Solution:

Height of solid cylinder = 4.5 cm

Volume of cylinder = 62.37 cu.cm

                 Π r² h = 62.37

  (22/7) x (r x (4.5) = 62.37

                      (r = 62.37 x (1/4.5) x (7/22)

                      (r = 13.86 x (7/22)

                      (r = (97.02)/22

                      (r = 4.41

                       r = √2.1 x 2.1

                       r = 2.1 cm

Radius of the cylinder = 2.1 cm


Question 5:

The radii of two right circular cylinders are in the ratio 2:3. Find the ratio of their volumes if their heights are in the ratio 5:3

Solution:

Let r₁ and r₂ are the radii of two cylinders

Let h₁ and h₂ are the heights of two cylinders

r₁ : r₂ = 2 : 3

r₁/r₂ = 2/3

r₁ = 2r₂/3

h₁ : h₂ = 5 : 3

h₁/h₂ = 5/3

h₁ = 5h₂/3

Volume of cylinder = Π r² h

Π r² h₁  : Π r² h₂ 

(2r₂/3)² (5h₂/3) : r² h₂

 (4r₂²/9)(5h₂/3) : r² h₂

  20/27 : 1

  20 : 27

Ratio of volume of two cylinders 20 : 27


Question 6:

The radius and height of two circular cylinders are in the ratio 5 : 7. If its volume is 4400 cu.cm,find the radius of the cylinder.

Solution:

Let r and h are the radius and height of cylinder

   r : h = 5 : 7

   r/h = 5/7

   r = 5h/7

 Volume of the cylinder = 4400 cu.cm

                         Π r² h = 4400

      (22/7) x (5h/7)² x h = 4400

      (22/7) x (25h²/49) x h = 4400

                                h³ = 4400 x (7/22) x (49/25)

                                h³ = 176 x (7/22) x (49)

                                h³ = 8  x 7 x 7 x 7

                                h³ = 2 x 2 x 2 x 7 x 7 x 7

                                h = 2 (7)

                                h = 14 cm

                                r = 5(14)/7

                                r = 5(2)

                                r = 10 cm

Radius of the cylinder = 10 cm

volume solution2 volume solution2