Answer:

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The surface area of the capsule is 20π mm^2.

Step-by-step explanation:

A capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends, so we can find the surface area of the capsule by finding the surface area of the cylinder and adding the surface area of the two hemispheres.

The surface area of the cylinder is given by the formula 2πr(h+r)

where r is the radius of the cylinder and h is the height of the cylinder.

In this case, the diameter of the capsule is 5mm, so the radius of the capsule is (5/2) mm, and the height of the capsule is 14 mm - 2 * (2r) = 14-4(5/2) = 2 mm

So the surface area of the cylinder is 2 * π * (5/2) * (2 + (5/2)) = 15π mm^2

The surface area of a hemisphere is given by the formula 2πr^2

where r is the radius of the hemisphere.

In this case, the radius of the hemisphere is (5/2) mm, so the surface area of each hemisphere is 2 * π * (5/2)^2 = 25π/4 mm^2

So the total surface area of the capsule is 15π mm^2 + 2 * (25π/4) mm^2 = 15π mm^2 + 25π/2 mm^2 = (40π/2) mm^2 = 20π mm^2

The surface area of the capsule is 20π mm^2.

Verified answer

Answer:

219.8 mm²

Step-by-step explanation:

radius of hemisphere is 5/2mm

height of cylinder is 14-(5/2+5/2)

c. s. a of cylinder is 2πrh

=2×3.14×5/2×9

15.7×9

=141.3mm²

c. s. a of 2 hemisphere is 2×2πr²

2×2×3.14×5/2×5/2

3.14×25

=78.5mm²

total area of capsule is

141.3+78.5

=219.8mm²

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