## 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