find the surface area of the figure below. A cylinder which has a hemisphere on one side of cylinder and radius is 5 and the hight is 8.
To find the surface area of the figure, we need to calculate the surface area of the cylinder and the surface area of the hemisphere separately, and then add them together.
1. Surface Area of the Cylinder:
The formula to calculate the surface area of a cylinder is given by:
SA_cylinder = 2πr_cylinder * h_cylinder
where r_cylinder is the radius of the cylinder and h_cylinder is the height of the cylinder.
Given that the radius of the cylinder is 5 and the height is 8, we can substitute these values into the formula:
SA_cylinder = 2π * 5 * 8
Calculating:
SA_cylinder = 2π * 40
SA_cylinder ≈ 251.33 square units
2. Surface Area of the Hemisphere:
The formula to calculate the surface area of a hemisphere is given by:
SA_hemisphere = 2πr_hemisphere^2
where r_hemisphere is the radius of the hemisphere.
Given that the radius of the hemisphere is 5, we can substitute this value into the formula:
SA_hemisphere = 2π * 5^2
Calculating:
SA_hemisphere = 2π * 25
SA_hemisphere ≈ 157.08 square units
3. Total Surface Area:
To find the total surface area, we add the surface area of the cylinder to the surface area of the hemisphere:
Total Surface Area = SA_cylinder + SA_hemisphere
Substituting the calculated values:
Total Surface Area = 251.33 + 157.08
Total Surface Area ≈ 408.41 square units
Therefore, the surface area of the figure is approximately 408.41 square units.
To find the surface area of the given figure, we need to calculate the surface area of the cylinder and the surface area of the hemisphere and then add them together.
1. Surface Area of the Cylinder:
The formula to find the surface area of a cylinder is given by:
Surface Area = 2πrh + 2πr^2
where:
- π is a mathematical constant (approximately equal to 3.14159)
- r is the radius of the cylinder
- h is the height of the cylinder
In this case, the radius (r) is given as 5, and the height (h) is given as 8. Substituting these values into the formula, we get:
Surface Area of Cylinder = 2π(5)(8) + 2π(5)^2
2. Surface Area of the Hemisphere:
The formula to find the surface area of a hemisphere is given by:
Surface Area = 2πr^2
where:
- π is a mathematical constant (approximately equal to 3.14159)
- r is the radius of the hemisphere
In this case, the radius (r) is given as 5. Substituting this value into the formula, we get:
Surface Area of Hemisphere = 2π(5)^2
3. Total Surface Area:
Since the surface area of the cylinder includes the curved surface area and the surface area of the bases, we need to subtract the surface area of one base from the total surface area of the cylinder:
Total Surface Area = Surface Area of Cylinder - Surface Area of Base + Surface Area of Hemisphere
= 2π(5)(8) + 2π(5)^2 - π(5)^2 + 2π(5)^2
Simplifying the equation, we get:
Total Surface Area = 2π(5)(8) + 2π(5)^2 + π(5)^2
Now, you can substitute the value of π (approximately equal to 3.14159) and calculate the surface area of the figure using a calculator. The final value will be the surface area of the given figure.