Question

if a cylinder and cone have equal radii and heights then find the ratio of their volumes​

Answer 1

❥$\:{\red{\underline{\underline{\large{\mathtt{GIVEN}}}}}}$

• A cylinder and cone have equal radii and height

❥$\:{\orange{\underline{\underline{\large{\mathtt{TO\:FIND}}}}}}$

• Ratio of their volumes

❥$\:{\purple{\underline{\underline{\large{\mathtt{SOLUTION}}}}}}$

Let,

• Radii of cylinder be r
• Height of cylinder be h

According to the given information

• Radii of cylinder = Radii of cone
• Height of cylinder = Height of cone

We know that,

• Volume of cylinder = πr²h
• Volume of cone = ⅓πr²h

Now,

→ Volume of cylinder : Volume of cone

→ πr²h : ⅓πr²h

→ 1 : ⅓

→ 1×3 : ⅓×3

→ 3 : 1

★ Hence, Ratio of their volumes is 3 : 1

Answer 2

QUESTION:-

✯.ɪғ ᴀ ᴄʏʟɪɴᴅᴇʀ ᴀɴᴅ ᴄᴏɴᴇ ʜᴀᴠᴇ ᴇϙᴜᴀʟ ʀᴀᴅɪɪ ᴀɴᴅ ʜᴇɪɢʜᴛs ᴛʜᴇɴ ғɪɴᴅ ᴛʜᴇ ʀᴀᴛɪᴏ ᴏғ ᴛʜᴇɪʀ ᴠᴏʟᴜᴍᴇs

ANSWER✔

$\Large\underline\bold{GIVEN,}$

$\sf\dashrightarrow THE\:RADII\:AND\: HEIGHT\:OF\:THE\:CONE\:AND\:CYLINDER\:ARE\:EQUAL$

$\Large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow RATIO\:OF\:VOLUME\:OF\:THE\:CYLINDER\:AND\:CONE$

Ratio of their volumes

$\Large\underline\bold{FORMULA\:USED,}$

$\sf\therefore volume\:of\:cylinder\: \pi r^2 h$

$\sf\therefore volume\:of\:cone\: \dfrac{1}{3} \pi r^2 h$

$\Large\underline\bold{SOLUTION,}$

$\sf\therefore let\:radii\:be\:'r'$

$\sf\therefore let\:height\:be\:'h'$

ACCORDING TO THE QUESTION,

$\sf\therefore radii\:of\:cylinder\:=radii\:of\:cone$

$\sf\therefore height\:of\: cylinder=height\:of\:cone$

$\sf\therefore volume\:of\:cylinder :volume\:of\:cone$

$\sf\therefore \pi r^2h: \dfrac{1}{3} \pi r^2h$

$\sf\therefore \cancel {\pi r^2h}: \dfrac{1}{3} \cancel {\pi r^2h}$

$\sf\therefore 1: \dfrac{1}{3}$

$\sf\therefore multiplying\:both\: sides\:by\:3$

$\sf\therefore 1 \times 3: \dfrac{1}{\cancel{3}} \times \cancel {3}$

$\sf\therefore 3:1$

$\sf\therefore \dfrac{volume\:of\:cylinder}{volume\:of\:cone} = \dfrac{3}{1}$

$\sf{\boxed{\sf{volume\:of\:cylinder: volume\:of\:cone= 3:1}}}$

__________________________

✯ADDITIONAL INFORMATION,

✯DIAGRAM OF CYLINDER:-

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✯DIAGRAM FOR CONE:-

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