The medicine capsule consists of a cylinder with a hemisphere at each end. The total length of the capsule is 18 millimeters. The diameter is 7 millimeters. Which choice is the best approximation of the total surface area of the capsule? Use 3.14 to approximate pi. possible answers a)396 square millimeters b)550 square millimeters c)1,407 square millimeters d)1,099 square millimeters

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05-04-2016
Mathematics

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The medicine capsule consists of a cylinder with a hemisphere at each end. The total length of the capsule is 18 millimeters. The diameter is 7 millimeters. Which choice is the best approximation of the total surface area of the capsule? Use 3.14 to approximate pi. possible answers a)396 square millimeters b)550 square millimeters c)1,407 square millimeters d)1,099 square millimeters

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meerkat18 meerkat18 · Answer 1 · 2016-04-07T23:10:02+02:00

Given:
diameter: 7 mm
total length = 18 mm

There are two shapes in this problem.
1) a sphere
2) a rectangle shaped cylinder

We need to get the area of both shapes to have the best approximation of the total surface area of the capsule.

Area of a sphere = 4 π r² = 4 * 3.14 * (3.5mm)² = 12.56 * 12.25mm²
Area of a sphere = 153.86 mm²

Area of a rectangle = length * width
*in this case, we need to compute for the circumference of the circle to get the measure of the width

Area of a rectangle = (18-7mm) * 7 * 3.14
Area of a rectangle = 11mm * 7mm * 3.14
Area of a rectagnle = 241.78 mm²

Total surface area = 153.86 mm² + 241.78 mm² = 395.64 mm²

Choice A.) 396 square millimeters.