Question

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

Answer 1

$\huge\underline\mathrm{SOLUTION:-}$

$\bf{\underline{\underline \orange{AnswEr:-}}}$

• Total surface area of capsule = 220 mm²

$\bf{\underline{\underline \orange{Given:-}}}$

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

$\bf{\underline{\underline \orange{Need\:To\:Find:-}}}$

• Total surface area of capsule = ?

$\bf{\underline{\underline \red{ExPlanation:-}}}$

Total area of the capsule = Curved surface area of cylinder + Curved surface area of 2 hemispheres

$\bf{\underline{\underline \pink{Curved\: Surface\:area\:of\: cylinder:-}}}$

Diameter of cylinder = 5 mm

Radius of cylinder = Diameter/2 = 5/2 mm

$\bf{\underline{\underline \green{Here:-}}}$

• Diameter of hemisphere = 5 mm

$\bf{\underline{\underline \green{So:-}}}$

• Radius of hemisphere = Diameter/2 = 5/2 mm

$\bf{\underline{\underline \green{Now:-}}}$

Height of cylinder + 2 × Radius of hemisphere = 14 mm

Height of cylinder = 14 - 2 × Radius of hemisphere

➠ 14 - 2 × 5/2

➠ 14 - 5

➠ 9 mm

$\bf{\underline{\underline \green{Now, Formula\:Used\:Here:-}}}$

• Curved surface area of cylinder = 2πrh

Putting the values according to the given formula:

➠ 2 × 22/7 × 5/2 × 9

➠ 22 × 45/7

➠ 990/7 mm²

$\bf{\underline{\underline \pink{Curved\: Surface\:area \:of \: hemisphere:-}}}$

• Radius of hemisphere = 5/2 mm

$\bf{\underline{\underline \green{Now, Formula\:Used\:Here:-}}}$

• Curved surface area of hemisphere = 2πr²

Putting the values according to the given formula:

➠ 2 × 22/7 × (5/2)²

➠ 2 × 22/7 × 5 × 5/5 × 5

➠ 11 × 5 × 5/7

➠ 275/7 mm²

Curved surface area of 2 hemispheres = 2 × area of hemisphere

➠ 2 × 275/7

➠ 550/7 mm²

Total area of the capsule = Curved surface area of cylinder + Curved surface area of 2 hemispheres

➠ 990/7 + 550/7

➠ 990 + 550/7

➠ 1540/7

➠ 220 mm²

$\bf{\underline{\underline \green{Hence:-}}}$

• $\dag$Total surface area of capsule is 220 mm²

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Answer 2

★Figure refer to attachment

$\Large{\underline{\underline{\bf{\purple{Given}}}}}$

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

• Length of capsule = 14mm
• Diameter of capsule = 5mm
• Radius of capsule = 5/2 mm

$\Large{\underline{\underline{\bf{\purple{Find\:out}}}}}$

• Surface area of capsule

$\Large{\underline{\underline{\bf{\purple{Solution}}}}}$

➞ Height of capsule

➞ Total length of capsule - 2 × radius of capsule

➞ 14 - 2 × 5/2

➞ 14 - 5 = 9mm

Therefore, height of capsule is 9mm

__________________________

Now, C.S.A of cylindrical part

$\implies\sf 2\pi{r}h \\ \\ \\ \implies\sf 2\times{\dfrac{22}{7}}\times{\dfrac{5}{2}}\times{9} \\ \\ \\ \implies\sf \dfrac{22}{7}\times{5}\times{9} \\ \\ \\ \implies\sf \dfrac{990}{7}\:sq.mm$

C.S.A of two hemispherical part

$\implies\sf 2\pi{r^2}+2\pi{r^2}=4\pi{r^2} \\ \\ \\ \implies\sf 4\times{\dfrac{22}{7}}\times{\dfrac{5}{2}}\times{\dfrac{5}{2}} \\ \\ \\ \implies\sf \dfrac{22}{7}\times{25} \\ \\ \\ \implies\sf \dfrac{550}{7}\:sq.mm$

___________________________

So, Surface area of capsule

➞ Curved surface area of cylindrical part + Curved surface area of hemispherical part

$\implies\sf \dfrac{990}{7}+\dfrac{550}{7} \\ \\ \\ \implies\sf \cancel\dfrac{1540}{7} = 220\:sq.mm$

${\underline{\boxed{\bf{\red{Hence,\:surface\:area\:of\:capsule=220\:sq.mm}}}}}$

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