A capsule is in the form of a cylinder with hemispherical ends. The to – InterviewSolution

1.

A capsule is in the form of a cylinder with hemispherical ends. The total height of the capsule is 19 cm and the diameter of the cylinder is 7cm. Find the volume of the capsule. A) 147 π cm³ B) 175.47 π cm³ C) 175.70 π cm³ D) 204.17 π cm³ Please explain step by step......

Answer»

GIVEN:

Total height of the capsule = 19 cm
Diameter of the cylinder is 7 cm

TO FIND:

What is the VOLUME of the capsule ?

SOLUTION:

❐ Diameter of the cylinder = 7 cm

Radius = Diameter/2 = 7/2 cm

❐ Total height of capsule = 19 cm

Height of cylinder = ( Total height –(radius of one HEMISPHERE + radius of another hemisphere)
Height of cylinder = ( 19– 3.5 + 3.5 ) = 12 cm

We know that the FORMULA for finding the volume of the cylinder is:-

$\large{\boxed{\bf{\star \: VOLUME= \pi r^2 h\: \star}}}$

We know that the formula for finding the Volume of Hemisphere is:-

$\large{\boxed{\bf{\star \: VOLUME = \dfrac{4}{3} \pi r^3 \: \star}}}$

According to question:-

$\large\bf{\star \: \pi r^2 h + \dfrac{4}{3} \pi r^3 + \dfrac{4}{3} \pi r^3 \: \star}$

$\sf{\longmapsto VOLUME = \pi r^2 \bigg( h + \dfrac{4}{3} r \bigg)}$

$\sf{\longmapsto VOLUME = \pi \times \bigg( \dfrac{7}{2} \bigg)^2 \times \bigg( 12 + \dfrac{4}{3} \times \dfrac{7}{2} \bigg) }$

$\sf{\longmapsto VOLUME = \pi \times \dfrac{49}{4} \Bigg( 12 + \dfrac{28}{6}\Bigg) }$

$\sf{\longmapsto VOLUME = \pi \times \dfrac{49}{4} \Bigg(\dfrac{72+28}{6} \Bigg) }$

$\sf{\longmapsto VOLUME = \pi \times \dfrac{49}{4} \times \dfrac{100}{6} }$

$\sf{\longmapsto VOLUME = \pi \times \cancel\dfrac{4900}{24}}$

$\bf{\longmapsto VOLUME = \pi \times 204.17 \: cm^3 }$

❝ Hence, the volume of capsule is 204.17π cm³ ❞

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