Question

A medicine capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. the length of the capsule is 14mm and the width is 5mm find its surface area​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• A medicine capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends.

Let assume that

• Radius of cylinder be r mm

• Height of cylinder be h mm.

As width of capsule is 5 mm

So, Radius of cylinder, r = 2.5 mm

As hemisphere stuck to each end of cylinder.

So, radius of hemisphere = r mm

Now, further given that length of capsule = 14 mm

So, it means

$\rm \: r + h + r = 14$

$\rm \: 2r + h = 14$

$\rm \: 2(2.5) + h = 14$

$\rm \: 5 + h = 14$

$\rm \: h = 14 - 5$

$\rm\implies \:h \: = \: 9 \: mm$

Now, Consider

$\rm \: Surface\:Area_{(Capsule)}$

$\rm \: = CSA_{(Hemisphere)} + CSA_{(Cylinder)} + CSA_{(Hemisphere)}$

$\rm \: = \: CSA_{(Cylinder)} + 2 \times CSA_{(Hemisphere)}$

$\rm \: = \: 2\pi \: rh \: + \: 2 \times 2\pi {r}^{2}$

$\rm \: = \: 2\pi \: r(h + 2r)$

$\rm \: = \: \dfrac{22}{7} \times 5 \times (9 + 5)$

$\rm \: = \: \dfrac{22}{7} \times 5 \times 14$

$\rm \: = \: 22 \times 5 \times 2$

$\rm \: = \: 220 \: {mm}^{2}$

Hence,

$\rm\implies \:\boxed{ \rm{ \:\rm \:Surface\:Area_{(Capsule)} = \: 220 \: {mm}^{2} \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Step-by-step explanation:

Given: Diameter of cylinder =5 mm

The radius of cylinder =2.5 mm

Height of cylinder =14-5=9 mm

Here, Diameter of hemisphere =5 mm

Radius of hemisphere =2.5 mm

So, The total area of the capsule = Curved Surface area of cylinder +Curved Surface area of two hemispheres

$\[ \begin{array}{l} \rm =2 \pi r h+2 \times 2 \pi r^{2} \\ \\ \rm =2 \pi r(h+2 r) \\ \\ \rm=2 \times \dfrac{22}{7} \times 2.5(9+5) \\ \\ \rm =220 mm ^{2} \end{array} \]$

Hence, the surface area of capsule is 220 mm².