Calculating the Total Surface Area of a Hemisphere

To find the total surface area of a hemisphere, we need to consider two parts: the curved surface area and the base area. Let's break down the calculation step-by-step:

Step 1: Understand the Properties of a Hemisphere
- A hemisphere is a three-dimensional shape that is half of a sphere.
- It has a curved surface that forms the rounded part of the hemisphere and a flat circular base at the bottom.

Step 2: Identify the Required Measurements
- We are given that the radius of the hemisphere is 10 cm.

Step 3: Calculate the Curved Surface Area
- The curved surface area of a hemisphere is half the surface area of a sphere.
- The formula for the surface area of a sphere is given by: A = 4πr^2, where r is the radius of the sphere.
- Therefore, the curved surface area of a hemisphere is: CSA = (1/2) * 4πr^2.

Substituting the given radius of the hemisphere (r = 10 cm) into the formula, we get:
CSA = (1/2) * 4π(10)^2
CSA = 200π cm^2

Step 4: Calculate the Base Area
- The base area of a hemisphere is a circle with radius equal to the radius of the hemisphere (r).
- The formula for the area of a circle is given by: A = πr^2.
- Therefore, the base area of a hemisphere is: BA = πr^2.

Substituting the given radius of the hemisphere (r = 10 cm) into the formula, we get:
BA = π(10)^2
BA = 100π cm^2

Step 5: Calculate the Total Surface Area
- The total surface area of a hemisphere is the sum of the curved surface area and the base area.
- Therefore, the total surface area (TSA) is given by: TSA = CSA + BA.

Substituting the calculated values of the curved surface area (CSA = 200π cm^2) and the base area (BA = 100π cm^2) into the formula, we get:
TSA = 200π + 100π
TSA = 300π cm^2

Step 6: Calculate the Final Result
- The final result will be the total surface area of the hemisphere.
- Using the value of π as approximately 3.14, we can calculate the numerical value of the total surface area.

Substituting π = 3.14 into the formula, we get:
TSA = 300 * 3.14
TSA ≈ 942 cm^2

Therefore, the total surface area of the hemisphere is approximately 942 cm^2.