Question

A medicine-capsule is in the shape of a cylinder of radius 0.25 cm with two hemispheres stuck to each of its ends. The length of the entire capsule is 2 cm. What is the total surface area of the capsule? (Take PIE as 3.14)

Please explain briefly

Answer 1

The total surface area of the capsule is 7.85 cm².

Step-by-step explanation:

To find the total surface area of the capsule, we need to calculate the areas of the cylinder and the two hemispheres. First, let's calculate the area of the cylinder:

Formula for the surface area of a cylinder is: SA = 2πr² + 2πrh

Given that the radius is 0.25 cm and the length is 2 cm:

SA of cylinder = 2 x 3.14 x (0.25)^2 + 2 x 3.14 x 0.25 x 2 = 1.57 + 3.14 = 4.71 cm²

Next, let's calculate the area of one hemisphere, and then double it to account for both hemispheres:

Formula for the surface area of a hemisphere is: SA = 2πr²

Given that the radius is 0.25 cm:

SA of one hemisphere = 2 x 3.14 x (0.25)^2 = 1.57 cm²

Since there are two hemispheres, the total surface area of the two hemispheres is 2 x 1.57 = 3.14 cm²

Finally, the total surface area of the capsule is the sum of the surface area of the cylinder and the surface area of the two hemispheres: 4.71 + 3.14 = 7.85 cm²

Answer 2

The total surface area of the capsule is 2.74 cm².

Step-by-step explanation:

To calculate the total surface area of the capsule, we need to find the surface area of the cylinder part and the two hemispheres. The surface area of the cylinder can be calculated using the formula:

A = 2πrh + 2πr²

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

Given that the radius of the cylinder is 0.25 cm and the height is 2 cm, we can plug these values into the formula:

A = 2π(0.25)(2) + 2π(0.25)²

Simplifying this expression, we get:

A = 1.57 + 0.39

A = 1.96 cm²

The surface area of each hemisphere is given by the formula:

A = 2πr²

Plugging in the radius of 0.25 cm, we get:

A = 2π(0.25)²

Simplifying this expression, we get:

A = 0.39 cm²

Since there are two hemispheres, the total surface area of the hemispheres is 2 times the surface area of one hemisphere:

Total Hemisphere Area = 2 × 0.39 cm² = 0.78 cm²

Adding the surface area of the cylinder and the total surface area of the hemispheres, we get:

Total Surface Area = Surface Area of Cylinder + Total Hemisphere Area

Total Surface Area = 1.96 cm² + 0.78 cm²

Total Surface Area = 2.74 cm²