Question

The radius and hieght of a cylinder are in the ratio 7:2. If the volume of the cylinder 8316 cm³, find the total surface area of the cylinder.
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Answer 1

FORMULA FOR VOLUME OF CYLINDER = pi X r^2 X h

Let the height be 2x

Radius = 7x

Volume = pi X 49x^2 X 2x = 3.14 X 98x^3 = 8316

x^3 = 8316 / 3.14*98 = 27.024567 cm

x = 3 cm

HEIGHT = 6 cm Radius = 21 cm

FORMULA FOR TOTAL SURFACE AREA = 2pirh + 2pir^2

= 2pir ( r + h)

= 2 X 3.14 X 21 X 27 = 3560.76 cm^2 ANSWER

Answer 2

Given :

⬤ Radius and Height of a Cylinder are in the Ratio 7:2 .

⬤ Volume of Cylinder is 8316 cm³ .

To Find :

⬤ Total Surface Area of Cylinder .

Formula Used :

$\bf[\:{Volume \: of \: Cylinder = \pi{r}^{2}h}\:]$

• r = radius
• h = height

Solution :

Let :

• Radius of Cylinder be = 7x .
• Height of Cylinder be = 2x .

Now :

8316 = πr²h

8316 = 22/7 × 7x × 7x × 2x

(8316 × 7) = 22 × 98x³

58212 = 2156x³

58212/2156 = x³

27 = x³

3 = x

Therefore , The Value of x is 3 .

Hence ,

Radius of Cylinder = 7x

= 7(3)

= 21

Height of Cylinder = 2x

= 2(3)

= 6

Therefore , Radius and Height of Cylinder is 21 cm and 6 cm.

Formula Used :

$\bf[\:{Total \: Surface \: Area \: of \: Cylinder = 2\pi{r}(r+h)}\:]$

• r = radius
• h = height

Now :

2πr (r + h)

2 × 22/7 × 21 (21 + 6)

44 × 3 (21 + 6)

132 (27)

3564

Therefore , Total Surface Area of Cylinder is 3564 cm² .