Question

3) Find the volume and surface areas of the
following cylinders given the circumference
of the base and height.
(i) C= 110 cm, h= 20 cm​

Answer 1

Answer:

Required surface area = 2200 cm²

Required volume of the cylinder = 19250 cm³.

Step-by-step explanation:

Given

Circumference of the base = 110 cm

Height of the cylinder = 20cm

Now -:

As the base is circular so

the circumference will be

$= > 2\pi \: r = 110 \\ = > 2 \times \frac{22}{7} \times r = 110 \\ = > \frac{44r}{7} = 110 \\ = > r = \frac{110 \times 7}{44} \\ = > r = \frac{ \cancel110 \times 7}{ \cancel44} \\ = > r = \frac{ \cancel10 \times 7}{ \cancel4} \\ = > r = \frac{35}{2} \\ = > \boxed{r =17.5cm}$

As the formula for the volume is πr²h

$=> \frac{22}{7} \times {(17.5)}^{2} \times 20 \\ = > \frac{22}{7} \times 17.5 \times 17.5 \times 20 \\ = > \frac{22}{ \cancel70} \times 175 \times 175 \times \cancel2 \\ = > \frac{22}{ \cancel35} \times \cancel175 \times 175 \\ = > 22 \times 5 \times 175 \\ = > 19250 {cm}^{3}$

And surface area is 2πrh

$= > 2 \times \frac{22}{7} \times 17.5 \times 20 \\ = > \frac{44 \times \cancel175 \times 2}{ \cancel7} \\ = > 44 \times 25 \times 2 \\ = > 2200 {cm}^{2}$

Answer 2

Answer:

∴ Total surface area of cylinder = 4125 cm²

∴ Curved surface area of Cylinder = 2200 cm²

∴ Volume of cylinder = 19250 cm³

Step-by-step explanation:

∴ Circumference of cylinder = 2πr

⇒ 110 = 2 × 22/7 × r

⇒ 110 × 7 = 44 × r

⇒ 770 = 44r

⇒ r = 770/44

⇒ r = 17.5 cm

Hence, radius of circle = 17.5 cm

Now, Total Surface area of cylinder =  2πr (h + r)

⇒ 2 × 22/7 × 17.5 (20 + 17.5)

⇒ 44/7 × 17.5 × 37.5

⇒ 28875/7

⇒ 4125 cm²

Hence, Total surface area of cylinder = 4125 cm²

Now, Curved surface area of cylinder = 2πrh

⇒ 2 × 22/7 × 17.5 × 20

⇒ 44/7 × 350

⇒ 15400/7

⇒ 2200 cm²

Hence, Curved surface area of Cylinder = 2200 cm²

Now, Volume of Cylinder = πr²h

⇒ 22/7 × 17.5 × 17.5 × 20

⇒ 134750/7

⇒ 19250 cm³

Hence, Volume of cylinder = 19250 cm³