A capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. If the length of the entire capsule is 12mm and the diameter of the capsule is 3mm, how much medicine it can hold
Answers
Step-by-step explanation:
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9th
Maths
Surface Areas and Volumes
Volume of a Sphere
A medicine capsule is in th...
MATHS
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. If the length of the cylindrical part of the capsule is 14mm and the diatmeter of hemisphere is 6mm, then find the volume of medicine capsule.
ANSWER
Given that:
Height of the cylindrical part of the capsule=14mm
Diameter of hemispherical part of the capsule=6mm
To find:
Volume of the medicine capsule=?
Solution:
Radius of hemispherical part of the capsule=3mm
Volume of the medicine capsule= Volume of cylindrical part of the capsule+ 2× Volume of hemispherical part of the capsule
=πr
2
h+2×
3
2
πr
3
=
7
22
×(3mm)
2
×14mm+2×
3
2
×
7
22
×(3mm)
3
Take (π=
7
22
)
=396mm
3
+113.143mm
3
=509.143mm
3
Therefore, Volume of the medicine capsule=509.143mm
3
Step-by-step explanation:
Length of Capsule (l) = 14 mm
Diameter of Capsule = Diameter of Cylinder =5 mm
Radius = 2Diameter
Therefore, Radius of each Hemisphere = Radius of Cylinder = r = 25 = 2.5 mm
Length of Cylinder = AB = Total length of Capsule - Radius of left Hemisphere - Radius of Right Hemisphere
=14−2.5−2.5=9 mm
Surface Area of Capsule = Curved Surface Area of Cylinder + Surface Area of Left Hemisphere + Surface Area of Right Hemisphere
=2πrl+2πr2+2πr2
=2πrl+4πr2
=2×722×2.5×9+4×722×2.52
=722[45+25]=722×70=220 mm2