Question

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them is being 3.5 cm and the total height of solid is 9.5 cm. Find the volume of the solid. (Use $(\pi=\frac{22}{7})$).

Answer 1

Answer:

The volume of the solid is 166.83 cm³.

Step-by-step explanation:

SOLUTION :  

Given:

Total height of the solid = 9.5 cm

Radius of the cone = Radius of the hemisphere = r = 3.5 cm

Radius of the hemisphere = height of hemisphere = 3.5 cm

Height of cone,( h) = Total height of the solid - height of hemisphere

h = 9.5 - 3.5 cm

Height of cone = 6cm

Volume of solid = volume of cone + volume of hemisphere

= 1/3πr²h + 2/3πr³

= 1/3πr²(h+2r)

= 1/3×22/7×3.5×3.5×(6 + 2×3.5)

= 1/3×22/7×3.5 × 3.5 × (6 + 7)

= 1/3×22/7×3.5×3.5×(13)

= 1/3×22×.5×3.5×(13)

= 500.5/3

Volume of solid = 166.83 cm³

Hence, the volume of the solid is 166.83 cm³.

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Answer 2

$\huge\bold\blue{Solution}$
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ɢɪᴠᴇɴ:

ᴛᴏᴛᴀʟ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ sᴏʟɪᴅ= 9.5 ᴄᴍ

ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ᴄᴏɴᴇ = ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ʜᴇᴍɪsᴘʜᴇʀᴇ = ʀ = 3.5 ᴄᴍ

ʀᴀᴅɪᴜs ᴏғ ᴛʜᴇ ʜᴇᴍɪsᴘʜᴇʀᴇ = ʜᴇɪɢʜᴛ ᴏғ ʜᴇᴍɪsᴘʜᴇʀᴇ = 3.5 ᴄᴍ

▌│█║▌║▌║ ║▌║▌║█│▌

ʜᴇɪɢʜᴛ ᴏғ ᴄᴏɴᴇ,( ʜ) =ᴛᴏᴛᴀʟ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ sᴏʟɪᴅ - ʜᴇɪɢʜᴛ ᴏғ ʜᴇᴍɪsᴘʜᴇʀᴇ

ʜ= 9.5- 3.5 ᴄᴍ

ʜ ᴏғ ᴄᴏɴᴇ =6ᴄᴍ

ᴠᴏʟᴜᴍᴇ ᴏғ sᴏʟɪᴅ = ᴠᴏʟᴜᴍᴇ ᴏғ ᴄᴏɴᴇ + ᴠᴏʟᴜᴍᴇ ᴏғ ʜᴇᴍɪsᴘʜᴇʀᴇ

= 1/3πʀ²ʜ+2/3πʀ³

= 1/3πʀ²(ʜ+2ʀ)

= 1/3×22/7×3.5×3.5×(6+2×3.5)

= 1/3×22/7×3.5×3.5×(6+7)

= 1/3×22/7×3.5×3.5×(13)

= 1/3×22×.5×3.5×(13)

= 500.5/3

= 166.83 ᴄᴍ³

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ʜᴇɴᴄᴇ, ᴛʜᴇ ᴠᴏʟᴜᴍᴇ ᴏғ ᴛʜᴇ sᴏʟɪᴅ ɪs 166.83 ᴄᴍ³

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