MATH SOLVE

2 months ago

Q:
# 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 5mm.Find its surface area.

Accepted Solution

A:

Diameter of the cylindrical portion of capsule = 5 mm

Length of the cylindrical portion of capsule = 14 mm - 5mm = 9 mm

Curved surface area of the cylindrical portion of capsule = [tex]2\pi \: rh[/tex]

[tex] = 2 \times \frac{22}{7} \times \frac{5}{2} \times 9 = \frac{990}{7} mm {}^{2} [/tex]

Curved surface area of two hemisphere =[tex]4\pi \: r {}^{2} [/tex]

[tex] = 4 \times \frac{22}{7} \times ( \frac{5}{2} ) {}^{2} [/tex]

[tex] = 4 \times \frac{22}{7} \times \frac{25}{4} = \frac{550}{7} mm {}^{2} [/tex]

Surface area of the capsule = Curved surface area of cylindrical portion + Curved surface area of hemispherical ends

[tex] = ( \frac{990}{7} + \frac{550}{7} ) \: mm {}^{2} = 220 \: mm {}^{2} [/tex]

Length of the cylindrical portion of capsule = 14 mm - 5mm = 9 mm

Curved surface area of the cylindrical portion of capsule = [tex]2\pi \: rh[/tex]

[tex] = 2 \times \frac{22}{7} \times \frac{5}{2} \times 9 = \frac{990}{7} mm {}^{2} [/tex]

Curved surface area of two hemisphere =[tex]4\pi \: r {}^{2} [/tex]

[tex] = 4 \times \frac{22}{7} \times ( \frac{5}{2} ) {}^{2} [/tex]

[tex] = 4 \times \frac{22}{7} \times \frac{25}{4} = \frac{550}{7} mm {}^{2} [/tex]

Surface area of the capsule = Curved surface area of cylindrical portion + Curved surface area of hemispherical ends

[tex] = ( \frac{990}{7} + \frac{550}{7} ) \: mm {}^{2} = 220 \: mm {}^{2} [/tex]