Question

The radius and the height of a cylinder are in the ratio 7:3 if the volume of the cylinder is 12474 cm cube find the curved surface area and the total surface area of the cylinder

Answer 1

Answer:

C. S. A = 1188cm²

T. S. A = 3960cm²

Step-by-step explanation:

Ratio = 7:3

Volume of cylinder = 12474 cm³

Let the given ratio = 7x and 3x

V. cylinder = πr²h

12474 = 22/7 × (7x)² × 3x

12474 = 22 × 21x³

12474 / 22 × 21 = x³

27 = x³

³√27 = x

3cm = x

Put the value of x in radius and height

7x = 7(3) = 21cm

3x = 3(3) = 9cm

C.S.A = 2πrh

2 × 22/7 × 21 × 9

2 × 22 × 3 × 9

44 × 27

1188cm²

T.S.A = 2πr(h + r)

2 × 22/7 × 21(9 + 21)

132 × 30

3960cm²

Answer 2

Answer:

Curved surface area of cylinder = 1188 cm² and Total surface area of cylinder = 3960 cm²

Step-by-step explanation:

Given :

The radius and height of a cylinder are in the ratio 7:3.

$\dfrac{r}{h}\:=\:\dfrac{7}{3}$

$r\:=\:\dfrac{7h}{3}$ ___ (eq 1)

Also,

Volume of cylinder = 12474 cm³

We know that..

Volume of cylinder = πr²h

Substitute the known values in above formula

⇒ $\dfrac{22}{7}\:\times\:\bigg( \dfrac{7}{3} \bigg)\:h\:=\:12474$

⇒ $\dfrac{154h^3}{9}\:=\:12474$

⇒ $154h^3\:=\:12474\:\times\:9$

⇒ $h^3\:=\:\dfrac{12475\:\times\:9}{154}$

⇒ $h^3\:=\:729$

⇒ $h\:=\:9$

(Height is 9 cm)

Substitute value of h in (eq 1)

⇒ $r\:=\:\dfrac{7(9)}{3}$

⇒ $r\:=\:21$

(Radius is 21 cm)

Now,

Curved surface area of cylinder = 2πrh

Substitute the known values in above formula

⇒ $2\:\times\:\dfrac{22}{7}\:\times\:21\:\times\:9$

⇒ $\dfrac{8136}{7}$

⇒ $\bold{1188}$ cm²

Total surface area of cylinder = 2πr(r + h)

Substitute the known values in above formula

⇒ $2\:\times\:\dfrac{22}{7}\:\times\:21(21+9)$

⇒ $\dfrac{924}{7}\:\times \:30$

⇒ $132\:\times\:30$

⇒ $\bold{3960}$ cm²