Question

$\textbf{\underline{Question}}}$ -

The volume of a cylinder of height 8cm is 1232 cm². Find the Curved surface area and the Total surface area.​

Answer 1

Answer:

The Total surface area is 660 cm² and Curved surface area is 352 cm².

Step-by-step explanation:

Given :

Volume = 1232 cm³

Height = 8 cm

To find :

Curved Surface Area and Total Surface area of the cylinder

Solution :

Let the radius be r

$\boxed{\sf{Volume= \pi r^{2}h}}$

$\tt{\implies} \: 1232 = \dfrac{22}{7} \times r \times r \times 8 \\ \\ \tt{\implies} \: 8624 = 176r^{2} \\ \\ \tt{\implies} \: {r}^{2} = \dfrac{8624}{176} \\ \\ \tt{\implies} \: {r}^{2} = 49 \\ \\ \tt{\implies} \: r = \sqrt{49} \\ \\ \tt{\implies} \: r = 7$

Radius = 7 cm

$\rule{300}{1.5}$

As we got the value of the cylinder's radius, we can now find the CSA and TSA.

★ $\textsf{\underline{\underline{Curved Surface Area -}}}$

$\boxed{\sf{Curved\: Surface\:Area=2 \pi rh}}$

$\tt{\implies} \: 2 \times \dfrac{22}{\cancel{7}} \times \cancel{7} \times 8 \\ \\ \tt{\implies} \: 2 \times 22 \times 8 \\ \\ \tt{\implies} \: 44 \times 8 \\ \\ \tt{\implies} \: 352 \: cm^{2}$

Curved Surface Area = 352 cm²

$\rule{300}{1.5}$

★ $\textsf{\underline{\underline{Total surface area -}}}$

$\boxed{\sf{Total\: Surface\:Area=2 \pi r(r+h)}}$

$\tt{\implies} \: 2 \times \dfrac{22}{\cancel{7}} \times \cancel{7}(7 + 8) \\ \\ \tt{\implies} \: 2 \times 22 \times (7 + 8) \\ \\ \tt{\implies} \: 44 \times 15 \\ \\ \tt{\implies} \: 660 \: {cm}^{2}$

Total Surface Area = 660 cm²

$\therefore$ The Total surface area is 660 cm² and Curved surface area is 352 cm².

Answer 2

Given,

• Height of the cylinder = 8cm
• Volume of the cylinder = 1232 cm²

To find,

• Curved surface area of cylinder?
• Total surface area of cylinder?

Formulae used,

• Volume of cylinder = πr²h
• Curved surface area of cylinder = 2πrh
• Total surface area of cylinder = 2πr(r + h)

Solution,

Firstly to find out the curved surface area of cylinder, we need to find the radius of cylinder, So let's use Volume of cylinder formula to find the radius of cylinder.

Volume of cylinder = πr²h

1232 = 22/7 × r² × 8

1232 = 25.14r²

r² = 1232/25.14

r² = 49

r = √49

r = 7 cm

We have got to know the value of radius, so next let's find out the Curved surface area of cylinder.

Curved surface area of cylinder = 2πrh

= 2 × 22/7 × 7 × 8

= 352cm²

Lastly, let's find out the Total surface area of cylinder.

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

= 2 × 22/7 × 7 (7+8)

= 660cm²

____________________________

• Curved surface area = 352cm²

• Total surface area = 660cm²