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 14 mm and the diameter of

the capsule is 5 mm. Find its surface area.​

Answer 1

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

Given that,

• 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 14 mm and the diameter of the capsule is 5 mm.

Let assume that

• Radius of hemispherical end be r mm

• Height of cylindrical part be h mm

As it is given that, diameter of capsule = 5 mm

So, radius, r = 2.5 mm

As, length of entire capsule = 14 mm

It means,

$r + h + r = 14$

$2r + h = 14$

$2 \times 2.5 + h = 14$

$5 + h = 14$

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

Now,

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

$\rm \: = \: 2 \times CSA_{(hemisphere)} + CSA_{(cylinder)}$

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

$\rm \: = \: 4\pi \: {r}^{2} + 2\pi \: rh$

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

$\rm \: = \: 2 \times \dfrac{22}{7} \times 2.5(2 \times 2.5 + 9)$

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

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

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

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

Hence,

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

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

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

Answer:

220mm²

Step-by-step explanation:

Radius of the Sphere =5/2mm

Let radius = 2.5mm

Cylinder height = Total height – Diameter of sphere

h = 14 – (2.5 + 2.5) = 9mm

Surface area of the capsule = CSA of cylinder + CSA of two hemispheres

= 2πrh + 2(2πr²)

= [2π(5/2)(9)] + 2[2π(5/2)²]

= 45π + 25π = 70π

= 70 × 22/7

= 220mm²

Hope my answer helps you :-)