Question

What is the surface area Round your answer to the nearest tenth and use 3.14 for pi Capsule Surface Area ? squared millimeters

Answer 1

648.8 mm^2

Explanation:

total surface area

=surface area of sphere + curve surface of cylinder

=4πr^2+2πrh

=4(3.14)(8.4/2)^2+2(3.14)(8.4/2)(16.2)

=648.8 mm^2 (nearest tenth)

Answer 2

The total surface area of the capsule is 290.1 square millimeters.

To calculate the surface area of a capsule, we need to consider both the cylindrical part and the hemispherical ends. Here are the steps:

1. Calculate the radius of the hemisphere and cylinder, which is half of the given diameter
`\( \text{radius} = \frac{8.4 \text{ mm}}{2} = 4.2 \text{ mm} \).`

2. Calculate the height of the cylindrical part. Since the total length of the capsule is the length of the cylinder plus the diameter of the two hemispheres, the height of the cylinder is the total length minus the diameter of one of the hemispheres:

`\( \text{cylinder height} = 15.2 \text{ mm} - 8.4 \text{ mm} = 6.8 \text{ mm} \).`

3. Calculate the surface area of the cylindrical part (excluding the ends, since they are hemispherical):

`\( \text{cylindrical surface area} = 2 \pi r * \text{height} = 2 * 3.14 * 4.2 * 6.8 \).`

4. Calculate the surface area of the two hemispheres. The surface area of a sphere is
`\( 4 \pi r^2 \)`, so for two hemispheres, it would be
`\( 2 \pi r^2 \):`

`\( \text{hemispherical surface area} = 2 * 3.14 * 4.2^2 \).`

5. Add the surface area of the cylindrical part and the surface area of the hemispheres to get the total surface area of the capsule.

6. Round the answer to the nearest tenth.

After calculating, we find that:

- The cylindrical surface area is approximately 179.36 square millimeters.

- The hemispherical surface area is approximately 110.78 square millimeters.

- The total surface area of the capsule is approximately 290.14 square millimeters.