Question

A conical tent of radius 7 cm and height 24cm is made of cardboard. Find area of cardboard required to make the tent.
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Answer 1

Given :-

• A conical tent of radius 7 cm and height 24cm is made of cardboard.

To find :-

• Area of cardboard required to make the tent.

Solution :-

• Radius of conical tent = 7cm

• Height of conical tent = 24cm

As we know that

→ Slant height = √(radius)² + (height)²

→ l = √r² + h²

→ l = √(7)² + (24)²

→ l = √49 + 576

→ l = √625

→ l = 25cm

Now,

Area of cardboard required to make conical tent = curved surface area of cone

→ Curved surface area of cone

→ πrl

Put the value of radius and slant height

→ 22/7 × 7 × 25

→ 22 × 25

→ 550cm²

Hence,

• Area of cardboard required to make the tent is 550cm²

Answer 2

GIVEN :-

• A ᴄᴏɴɪᴄᴀʟ ᴛᴇɴᴛ ᴏғ ʀᴀᴅɪᴜs 7 ᴄm .

• Hᴇɪɢʜᴛ = 24 cm .

• Tʜɪs ʀᴇǫᴜɪʀᴇᴍᴇɴᴛs ᴍᴀᴅᴇ ᴀ ᴄᴀʀᴅʙᴏᴀʀᴅ .

TO FIND :-

• Tʜᴇ ᴀʀᴇᴀ ᴏғ ᴄᴀʀᴅʙᴏᴀʀᴅ ʀᴇǫᴜɪʀᴇᴅ ᴛᴏ ᴍᴀᴋᴇ ᴛʜᴇ ᴛᴇɴᴛ .

SOLUTION :-

☯︎ Aʀᴇᴀ ᴏғ ᴄᴀʀᴅʙᴏᴀʀᴅ = Cᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴛʜᴇ ᴄᴏɴɪᴄᴀʟ ᴛᴇɴᴛ

$\huge\orange\star$ Cᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ = $\bf\pink{\pi\:r\:l\:}$

Wʜᴇʀᴇ,

• r = ʀᴀᴅɪᴜs

• l = sʟᴀɴᴛ ʜᴇɪɢʜᴛ

$\huge\blue\checkmark$ $\bf\red{l\:=\:\sqrt{r^2\:+\:h^2}}$

$\rm{\implies\:l\:=\:\sqrt{7^2\:+\:(24)^2}}$

$\rm{\implies\:l\:=\:\sqrt{49\:+\:576}}$

$\rm{\implies\:l\:=\:\sqrt{625}}$

$\bf\green{\implies\:l\:=\:25\:cm\:}$

✰ Nᴏᴡ ᴛʜᴇ ᴀʀᴇᴀ ᴏғ ᴛʜᴇ ᴄᴀʀᴅʙᴏᴀʀᴅ ɪs,

➟ Cᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ = $\bf\pink{\pi\:r\:l\:}$

➪ ᴄ.s.Aʀᴇᴀ = 22/7 × 7 × 25

➪ ᴄ.s.Aʀᴇᴀ = 550 cm²

$\huge\red{\therefore}$ Tʜᴇ ᴀʀᴇᴀ ᴏғ ᴄᴀʀᴅʙᴏᴀʀᴅ ʀᴇǫᴜɪʀᴇᴅ ᴛᴏ ᴍᴀᴋᴇ ᴛʜᴇ ᴛᴇɴᴛ ɪs "550 cm²" .