Question

Calculate the total surface area area and curved surface area of cylinder of radius 7 cm and height 21 cm.​

Answer 1

$\large{\red{\bold{\underline{Given:}}}}$

$\sf \: Radius \: of \: the \: cylinder = 7 cm \\ \\ \sf \: Height \: of \: cylinder = 21cm$

$\large{\green{\bold{\underline{To \: Find:}}}}$

$\sf \: (i) \: Total \: surface \: area \: of \: cylinder \\ \\ \sf \: (ii) \: Curved \: surface \: area \: of \: cylinder$

$\large{\blue{\bold{\underline{Formula \: Used:}}}}$

$\sf \: Total \: surface \: area = 2\pi r(r + h) \\ \\ \sf \: Curved \: surface \: area = 2\pi rh$

$\large{\red{\underline\bold{{Solution:}}}}$

$\sf \: Let \: the \: radius \: of \: the \: cylinder \: be \: r, \\ \sf \: and \: the \: height \: of \: the \: cylinder \: as \: h$

$\large{\green{\bold{\underline{Then:}}}}$

$\sf \: (i) \: Total \: surface \: area = 2\pi r(r + h) \\ \\ \rightarrow \: \sf Total \: surface \: area = 2 \times \frac{22}{7} \times 7(7 + 21) \\ \\ \rightarrow \: \sf Total \: surface \: area = 2 \times \frac{22}{7} \times 7(28) \\ \\ \rightarrow \: \sf \: Total \: surface \: area = \frac{44}{\cancel7} \times \cancel7 \times 28 \\ \\ \rightarrow \: \sf \: Total \: surface \: area = 1232 \: {cm}^{2}$

$\large{\pink{\bold{\underline{Now:}}}}$

$\sf \: (ii) \: Curved \: surface \: area = 2\pi rh \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 2 \times \frac{22}{7} \times 7 \times 21 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 2 \times \frac{22}{\cancel7} \times \cancel7 \times 21 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 44 \times 21 \\ \\ \rightarrow \: \sf \: Curved \: surface \: area = 924 \: {cm}^{2}$

$\large{\orange{\bold{\underline{Therefore:}}}}$

$\sf \: The \: total \: surface \: area \: of \: cylinder \: is \\ \sf \: 1232 {cm}^{2} \: and \: curved \: surface \: area \: is \: 924 {cm}^{2}.$

Answer 2

GIVEN :-

• Rᴀᴅɪᴜs ᴏғ ᴄʏʟɪɴᴅᴇʀ = 7 ᴄm

• Hᴇɪɢʜᴛ ᴏғ ᴄʏʟɪɴᴅᴇʀ = 21 ᴄm

TO FIND :-

1. Tᴏᴛᴀʟ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ .
2. Cᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ .

SOLUTION :-

$\huge\orange\star$ Tᴏᴛᴀʟ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ = $\bf\pink{2\:\pi\:r\:(r\:+\:h)\:}$

Wʜᴇʀᴇ,

• r = 7 cm

• h = 21 cm

➪ ᴛ.s.ᴀ = 2 × 22/7 × 7 × (7 + 21)

➟ ᴛ.s.ᴀ = 44 × 28

➟ ᴛ.s.ᴀ = 1232 cm²

$\huge\bf\red{\therefore}$ Tʜᴇ ᴛᴏᴛᴀʟ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅᴇʀ ɪs "1232 cm²".

$\rule{200}2$

$\huge\green\star$ Cᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ = $\bf\pink{2\:\pi\:r\:h\:}$

Wʜᴇʀᴇ,

• r = 7 cm

• h = 21 cm

➪ ᴄ.s.ᴀ = 2 × 22/7 × 7 × 21

➟ ᴄ.s.ᴀ = 44 × 21

➟ ᴄ.s.ᴀ = 924 cm²

$\huge\bf\red{\therefore}$ Tʜᴇ ᴄᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴛʜᴇ ᴄʏʟɪɴᴅᴇʀ ɪs "924 cm²" .