Question

༒@ Mᴏᴅᴇʀᴀᴛᴏʀs!!
@ Bʀᴀɪɴʟʏ Sᴛᴀʀs!!
@ Bʀᴀɪɴʟʏ Usᴇʀs!!༒

༒Mᴀᴛʜs Cʜᴀᴘᴛᴇʀ 13:- Sᴜʀғᴀᴄᴇ Aʀᴇᴀ Aɴᴅ Vᴏʟᴜᴍᴇ༒

☛A ᴍᴇᴅɪᴄɪɴᴇ ᴄᴀᴘsᴜʟᴇ ɪs ɪɴ ᴛʜᴇ sʜᴀᴘᴇ ᴏғ ᴀ ᴄʏʟɪɴᴅᴇʀ ᴡɪᴛʜ ᴛᴡᴏ ʜᴇᴍɪsᴘʜᴇʀᴇs sᴛᴜᴄᴋ ᴛᴏ ᴇᴀᴄʜ ᴏғ ɪᴛs ᴇɴᴅs. Tʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴇɴᴛɪʀᴇ ᴄᴀᴘsᴜʟᴇ ɪs 14 ᴍᴍ ᴀɴᴅ ᴛʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴄᴀᴘsᴜʟᴇ ɪs 5 ᴍᴍ. Fɪɴᴅ ɪᴛs Sᴜʀғᴀᴄᴇ Aʀᴇᴀ.

☞Iᴍᴘᴏʀᴛᴀɴᴛ ɴᴏᴛɪᴄᴇ ☟

☛ Nᴏ sᴘᴀᴍ...
☛ Nᴏ Wᴇʙsɪᴛᴇs Aɴsᴡᴇʀs...
☛ Wᴇʙsɪᴛᴇs/Sᴘᴀᴍ ᴡɪʟʟ ʙᴇ ʀᴇᴘᴏʀᴛᴇᴅ ᴏɴ ᴛʜᴇ Sᴘᴏᴛ...
☛ Tɪᴍᴇ Lɪᴍɪᴛ:- 15 ᴍɪɴ.


☞Aʟʟ ᴛʜᴇ Bᴇsᴛ :)​

Answer 1

Question :

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends . The length of the entire capsule is 14mm and the diameter of the capsule is 5 mm. Find its surface area .

Solution :

Let us rotate the figure perpendicularly and remove the hemispherical parts; we will get something similar to this.

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{2.5 \: mm }}\put(9,17.5){\sf{9 \: mm}}\end{picture}$

• The height of the cylinder = 14 mm - 2×5/2 mm = 14 - 5 mm = 9 mm

• The radius of the cylinder = 2.5 mm

LSA of cylinder = 2πrl = 2 × 3.14 × 2.5 × 9 = 141.3 mm²

Now , LSA of the two hemispherical domes combined -

> 2πr² + 2πr² = 4πr²

> 4 × 3.14 × 2.5 × 2.5

> 78.5 mm²

Total surface area of the figure -

> 141.3 mm² + 78.5 mm²

> 219.8 mm² .

Answer : The total surface area of the given figure is 219.88 mm² .

╰─━━━━━━━━━━━━─╯

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ Formulae&\bf Surface\ area\ Formulae\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

╭─━━━━━━━━━━━━─╮

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$

╰─━━━━━━━━━━━━─╯

Note : Some of the latex figures aren't visible in app . Please check out from web . https://brainly.in/question/42082664

_______________________________________

Answer 2

Given :-

A ᴍᴇᴅɪᴄɪɴᴇ ᴄᴀᴘsᴜʟᴇ ɪs ɪɴ ᴛʜᴇ sʜᴀᴘᴇ ᴏғ ᴀ ᴄʏʟɪɴᴅᴇʀ ᴡɪᴛʜ ᴛᴡᴏ ʜᴇᴍɪsᴘʜᴇʀᴇs sᴛᴜᴄᴋ ᴛᴏ ᴇᴀᴄʜ ᴏғ ɪᴛs ᴇɴᴅs. Tʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴇɴᴛɪʀᴇ ᴄᴀᴘsᴜʟᴇ ɪs 14 ᴍᴍ ᴀɴᴅ ᴛʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴄᴀᴘsᴜʟᴇ ɪs 5 ᴍᴍ.

To Find :-

SA

Solution :-

Radius = Diameter/2

Radius = 5/2

Radius = 2.5 mm

There are 2 hemisphere. So, Length left = 14 - 2(2.5)

14 - 5

9 mm

Now

SA of the capsule = 2πrl + 2πr² + 2πr²

SA of the capsule = 2πrl + 4πr²

SA of the capsule = 2 × 22/7 × 2.5 × 9 + 4 × 22/7 × (2.5)²

SA of the capsule = 44/7 × 2.5 × 9 + 88/7 × 6.25

SA of the capsule = 990/7  + 550/7

SA of the capsule = 1440/7

SA of the capsule = 220 mm²