find the total area of the surface of a solid hemisphere of diameter 6.6?
well, the area of a sphere of diameter d is πd^2
so, what do you think?
(don't forget the flat part...)
Find the total area of the surface of a solid hemisphere of a diameter of 6.6cm
To find the total surface area of a solid hemisphere, we need to calculate the curved surface area of the hemisphere and add it to the base area of the hemisphere.
Step 1: Calculate the radius of the hemisphere.
The diameter of the hemisphere is given as 6.6 units. The radius of a sphere or a hemisphere is half its diameter. So, divide the given diameter by 2:
Radius = Diameter / 2 = 6.6 / 2 = 3.3 units.
Step 2: Calculate the curved surface area of the hemisphere.
The curved surface area of a hemisphere is given by the formula: A = 2πr^2, where r is the radius.
Substituting the value of the radius into the formula:
Curved Surface Area = 2 * π * (3.3)^2
Step 3: Calculate the base area of the hemisphere.
The base area of a hemisphere is the area of a circle with radius r. The formula is A = πr^2.
Substituting the value of the radius into the formula:
Base Area = π * (3.3)^2
Step 4: Add the curved surface area and the base area.
Total Surface Area = Curved Surface Area + Base Area
Now, let's calculate the values.
Curved Surface Area = 2 * π * (3.3)^2
Base Area = π * (3.3)^2
Total Surface Area = Curved Surface Area + Base Area
Total Surface Area = 2 * π * (3.3)^2 + π * (3.3)^2
= 2π * (3.3)^2 + π * (3.3)^2
= π * [(2 * (3.3)^2) + (3.3)^2]
= π * [(2 * 10.89) + 10.89]
= π * (21.78 + 10.89)
= π * 32.67
≈ 102.41 square units.
Therefore, the total area of the surface of the solid hemisphere is approximately 102.41 square units.