Question

6. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to eachof its ends (see Fig. 13.10). The length ofthe entire capsule is 14 mm and the diameterof the capsule is 5 mm. Find its surface area.​

Answer 1

Answer:

surface area 219,8mm²

Scylinder = L*h

because diameter 5mm

h cylinder = 14-5 = 9mm

L = Pi*D

L = 3,14*5=15,7mm

Scylinder = 15,7*9 = 141,3 mm²

2 hemispheres = 1 sphere

Ssphere=4* Pi*R²

R=D/2   R=5/2  R=2,5mm

Ssphere=4* 3,14*2,5*2,5

Ssphere=78,5mm²

Scapsule = Scylinder+Ssphere

Scapsule = 141,3+78,5

Scapsule = 219,8mm²

Answer 2

Answer:   S = 70$\pi$ = 219.8 $mm^{2}$;

S = S1 + S2 +S3;

S1 + S3 = $4\pi R^{2} ;$   surface of a sphere (2 hemispheres = 1 sphere)

S2 = $2\pi Rh$;           lateral surface of the cylinder;

R = 5 / 2 = 2.5 mm;

h = 14 - 2 * 2.5 = 9 mm;

S = 4$\pi$*2.5*2.5 + 2$\pi$*2.5*9 = 25$\pi$ + 45$\pi$ = 70$\pi$ = 219.8 $mm^{2}$.

Answer 3

To find the surface area of the medicine capsule, you can break it down into its different components: the cylindrical part and the two hemispheres. Then, calculate the surface area of each part separately and add them together.

1. Surface Area of the Cylinder: The formula for the lateral surface area of a cylinder is given by: Lateral Surface Area = 2πrh where:

   • r is the radius of the cylinder
   • h is the height of the cylinder

   In this case, the diameter of the capsule is given as 5 mm, so the radius (r) is half of that, which is 5 mm / 2 = 2.5 mm = 0.25 cm. The height (h) of the cylindrical part is the length of the entire capsule minus the sum of the two hemispheres' radii. Each hemisphere has a radius of 0.25 cm.

   So, the height of the cylindrical part = 14 mm - (2 * 0.25 cm) = 14 mm - 0.5 cm = 13.5 mm = 1.35 cm.

   Now, calculate the lateral surface area of the cylinder: Lateral Surface Area = 2π * 0.25 cm * 1.35 cm = 2 * π * 0.25 cm * 1.35 cm ≈ 2.13 cm²

2. Surface Area of a Hemisphere: The formula for the surface area of a hemisphere is given by: Surface Area = 2πr² where:

   • r is the radius of the hemisphere

   In this case, the radius of each hemisphere is 0.25 cm (as calculated above). So, for one hemisphere: Surface Area of one hemisphere = 2π * (0.25 cm)² = π * 0.0625 cm² ≈ 0.196 cm²

   Since there are two hemispheres, the total surface area of the two hemispheres is 2 times this value: Total Surface Area of two hemispheres = 2 * 0.196 cm² ≈ 0.392 cm²

3. Add the Surface Areas of the Components: Now, add the surface area of the cylindrical part to the total surface area of the two hemispheres: Total Surface Area = Lateral Surface Area of Cylinder + Total Surface Area of two Hemispheres Total Surface Area ≈ 2.13 cm² + 0.392 cm² ≈ 2.522 cm²

So, the surface area of the medicine capsule is approximately 2.522 square centimeters.