Question

a cuboid equal block of side 7 cm is surmounted by a hemisphere what was the greatest diameter the hemisphere can have find the surface area of solid

Answer 1

$\displaystyle \sf{ \purple { Correct \: Question \: - }}$

ᴀ ᴄᴜʙɪᴄᴀʟ ʙʟᴏᴄᴋ ᴏꜰ ꜱɪᴅᴇ 7 ᴄᴍ ɪꜱ ꜱᴜʀᴍᴏᴜɴᴛᴇᴅ ʙʏ ᴀ ʜᴇᴍɪꜱᴘʜᴇʀᴇ ᴏꜰ ᴅɪᴀᴍᴇᴛᴇʀ ᴇQᴜᴀʟ ᴛᴏ ᴛʜᴇ ꜱɪᴅᴇ ᴏꜰ ᴛʜᴇ ᴄᴜʙᴇ.

ꜰɪɴᴅ ᴛʜᴇ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴛʜᴇ ꜱᴏʟɪᴅ .

$\displaystyle \tt{ \orange { \underline { \underline { \star Solution \: - }}}}$

The required diagram \lor $\lor$

$\displaystyle \orange{ \setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(-3,1.5)(0,0)(3,1.5)\qbezier(-3,1.5)(-2.5,4)(0,4.2)\qbezier(3,1.5)(2.5,4)(0,4.2)\put(-3.5,-4.3){\framebox(6,5)}\qbezier(-3.5,0.7)(-3.5,0.7)(-3,1.5)\multiput(2.5,-4.3)(0,5){2}{\line(2,3){1.5}}\put(4,-2.05){\line(0,1){5}}\put(4,2.95){\line(-1,0){1.5}}\multiput(-3,1.5)(0.3,0){20}{\line(1,0){0.2}}\put(-0.5,2){\bf 7 \ cm}\put(-3.3,0){\vector(1,0){5.7}}\put(-3.3,0){\vector(-1,0){0.1}}\put(-0.9,-0.6){\bf 7 \ cm}\end{picture} }$

The side of the cuboidal box is 7 cm .

This is the largest possible diameter of the hemisphere , 7 cm

We have to find the surface area of the solid .

To find this :

> Surface Area of Cube + Curved surface area of hemisphere - Area of base of hemisphere .

> 6 r² + 2π r² - π r²

> 6 r² + π r²

> ( 6 + π ) r²

> ( 6 + 22/7 ) × 7 × 7

> [ 42 + 22 ] × 7

> 64 × 7

> 448 cm² .

This is the required answer .

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Answer 2

Answer:

$\displaystyle \sf{ \purple { Correct \: Question \: - }}CorrectQuestion−</p><p></p><p>ᴀ ᴄᴜʙɪᴄᴀʟ ʙʟᴏᴄᴋ ᴏꜰ ꜱɪᴅᴇ 7 ᴄᴍ ɪꜱ ꜱᴜʀᴍᴏᴜɴᴛᴇᴅ ʙʏ ᴀ ʜᴇᴍɪꜱᴘʜᴇʀᴇ ᴏꜰ ᴅɪᴀᴍᴇᴛᴇʀ ᴇQᴜᴀʟ ᴛᴏ ᴛʜᴇ ꜱɪᴅᴇ ᴏꜰ ᴛʜᴇ ᴄᴜʙᴇ.</p><p></p><p>ꜰɪɴᴅ ᴛʜᴇ ꜱᴜʀꜰᴀᴄᴇ ᴀʀᴇᴀ ᴏꜰ ᴛʜᴇ ꜱᴏʟɪᴅ .</p><p></p><p>\displaystyle \tt{ \orange { \underline { \underline { \star Solution \: - }}}}⋆Solution−</p><p></p><p>The required diagram \lor \lor∨</p><p></p><p>\displaystyle \orange{ \setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(-3,1.5)(0,0)(3,1.5)\qbezier(-3,1.5)(-2.5,4)(0,4.2)\qbezier(3,1.5)(2.5,4)(0,4.2)\put(-3.5,-4.3){\framebox(6,5)}\qbezier(-3.5,0.7)(-3.5,0.7)(-3,1.5)\multiput(2.5,-4.3)(0,5){2}{\line(2,3){1.5}}\put(4,-2.05){\line(0,1){5}}\put(4,2.95){\line(-1,0){1.5}}\multiput(-3,1.5)(0.3,0){20}{\line(1,0){0.2}}\put(-0.5,2){\bf 7 \ cm}\put(-3.3,0){\vector(1,0){5.7}}\put(-3.3,0){\vector(-1,0){0.1}}\put(-0.9,-0.6){\bf 7 \ cm}\end{picture} }</p><p></p><p>The side of the cuboidal box is 7 cm .</p><p></p><p>This is the largest possible diameter of the hemisphere , 7 cm</p><p></p><p>We have to find the surface area of the solid .</p><p></p><p>To find this :</p><p></p><p>> Surface Area of Cube + Curved surface area of hemisphere - Area of base of hemisphere .</p><p></p><p>> 6 r² + 2π r² - π r²</p><p></p><p>> 6 r² + π r²</p><p></p><p>> ( 6 + π ) r²</p><p></p><p>> ( 6 + 22/7 ) × 7 × 7</p><p></p><p>> [ 42 + 22 ] × 7</p><p></p><p>> 64 × 7</p><p></p><p>> 448 cm² .</p><p></p><p>This is the required answer .</p><p></p><p>--------------------------------------------------------------------------------------</p><p></p><p>$