## Curved Surface Area Solution3

In this page curved surface area solution3 we are going to see solution of some practice questions.

Question 6

The total surface area of a solid right circular cylinder is 1540 cm². If the height is four times the radius of the base, then find the height of the cylinder.

Solution:

Total surface area of cylinder = 1540 cm²

2 Π r (h + r) = 1540

h = 4 x radius of the base

h = 4 r

2 Π r (4 r + r) = 1540

2 Π r (5 r) = 1540

2 x (22/7) x 5 r² = 1540

= 1540 x (1/2) x (7/22) x (1/5)

= (1540 x 7)/(2 x 22 x 5)

= (1540 x 7)/(2 x 22 x 5)

r² = 49

r = √7x 7

r = 7 cm

height  = 4 (7)

= 28 cm

Height of the cylinder = 28 cm

Question 7

The radii of two right circular cylinders are in the ratio 3:2 and their heights are in the ratio 5:3. Find the ratio of their curved surface areas.

Solution:

Let r₁ , r₂ and h₁ , h₂ are radii and heights of first and second cylinders respectively.

Now we have to find the ratio of their curved surface areas

Curved surface area of cylinder = 2 Π r h

Curved surface area of first cylinder = 2 Π r₁ h₁

Curved surface area of first cylinder = 2 Π r₂ h₂

r₁ : r₂ = 3 : 2

r₁/r₂ = 3/2

r₁= 3r₂/2

h₁ : h₂ = 5 : 3

h₁/h₂ = 5/3

h₁= 5h₂/3

Ratios of curved surface area of two cylinders

2 Π r₁ h₁  :   2 Π r₂ h₂

(3r₂/2) (5h₂/3) :  r₂ h₂

5/2 : 1

5 : 2

curved surface area solution3 curved surface area solution3