6. 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.
Answers
Step-by-step explanation:
Two hemisphere and one cylinder are shown in the figure given below.
Here, the diameter of the capsule = 5 mm
∴ Radius = 5/2 = 2.5 mm
Now, the length of the capsule = 14 mm
So, the length of the cylinder = 14-(2.5+2.5) = 9 mm
∴ The surface area of a hemisphere = 2πr2 = 2×(22/7)×2.5×2.5
= 275/7 mm2
Now, the surface area of the cylinder = 2πrh
= 2×(22/7)×2.5×9
(22/7)×45 = 990/7 mm2
Thus, the required surface area of medicine capsule will be
= 2×surface area of hemisphere + surface area of the cylinder
= (2×275/7) × 990/7
(550/7) + (990/7) = 1540/7 = 220 mm2
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Answer:
Length of Capsule (l) = 14 mm
Diameter of Capsule = Diameter of Cylinder =5 mm
Radius =
2
Diameter
Therefore, Radius of each Hemisphere = Radius of Cylinder = r =
2
5
= 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+2πr
2
+2πr
2
=2πrl+4πr
2
=2×
7
22
×2.5×9+4×
7
22
×2.5
2
=
7
22
[45+25]=
7
22
×70=220 mm
2