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Maths Chapter 13:- Surface Areas And Volumes..

☛A cubical block of side 7cm is surmounted on a hemisphere of same radius. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

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Answer 1

$ANSWER \:$

The greatest diameter=side of the cube=7cm.

The greatest diameter=side of the

$= 6side {}^{2} \:$

$= 6 \times 7 \times 7$

$= 294sqcm$

Surface area of bese of hemisphere is,

$\pi \: r {}^{2}$

$= \frac{22}{7} \times 3.5 {}^{2}$

$38.5cm {}^{2}$

Curved Surface Area of hemisphere is,

$= 2 \times 38.5$

$77sqcm$

∴Total surface area is =294-38.5+77

$= 332.5sqcm$

Hope it helps you

Answer 2

{\__/}

(• ◡ • )

/<❤>✨ANSWER☃️✨

(ɪ) ᴀ ᴄᴜʙɪᴄᴀʟ ʙʟᴏᴄᴋ ᴏғ sɪᴅᴇ 7 ᴄᴍ ɪs sᴜʀᴍᴏᴜɴᴛᴇᴅ ʙʏ ᴀ ʜᴇᴍɪsᴘʜᴇʀᴇ.

∴ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ʜᴇᴍɪsᴘʜᴇʀᴇ ɪs = 7 ᴄᴍ.

ʀᴀᴅɪᴜs ᴏғ ʜᴇᴍɪsᴘʜᴇʀᴇ, ʀ = 3.5 ᴄᴍ.

∴ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ʜᴇᴍɪsᴘʜᴇʀᴇ = ᴄᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ – ᴀʀᴇᴀ ᴏғ ʙᴀsᴇ ᴏғ ʜᴇᴍɪsᴘʜᴇʀᴇ

$➢ \: 2\pi \: {r}^{2} - \pi {r}^{2}$

$➠ \: 2 \times \frac{22}{7} \times ({ \frac{7}{2} })^{2} \times \frac{22}{7} \times ({ \frac{7}{2} })^{2}$

(ɪɪ) ᴛʜᴇ ᴄᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ sǫᴜᴀʀᴇ,

=6 × l^2

= 6 × (7)^2

= 6 × 49 = 294 sǫ. ᴄᴍ.

∴ ᴛᴏᴛᴀʟ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴄᴜʙɪᴄᴀʟ ʙʟᴏᴄᴋ, = ᴄᴜʀᴠᴇᴅ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴄᴜʙɪᴄᴀʟ ʙʟᴏᴄᴋ + sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ʜᴇᴍɪsᴘʜᴇʀᴇ.

= 294 + 38.5

= 332.5sǫ.ᴄᴍ.

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