What is the surface area of a right circular cylinder topped with hemisphere if the height is 60ft and the length is 20ft?
Formula has three parts because this is an enclosed structure - the area of the hemisphere, the area of the cylinder, and the area of the circular bottom of the cylinder.
Therefore:
A = 2PiR^2 + 2PiRH + PiR^2
R = radius of cylinder and sphere
H = height of cylinder
A = 2PiRH + 2PiR^2
To calculate the surface area of a right circular cylinder topped with a hemisphere, we need to find the individual surface areas of the cylinder and the hemisphere first, and then add them.
1. Surface area of the cylinder:
The formula to calculate the surface area of a cylinder is given by 2πrh, where r is the radius and h is the height. In this case, the height is given as 60ft, and the length is given as 20ft. The radius can be calculated as half of the length. So, the radius (r) = 20ft / 2 = 10ft.
The surface area (A) of the cylinder can be calculated as:
A = 2πrh
A = 2π(10ft)(60ft)
A = 1200π square feet
2. Surface area of the hemisphere:
The formula to calculate the surface area of a hemisphere is given by 2πr^2, where r is the radius. In this case, the radius is the same as that of the cylinder, which is 10ft.
The surface area (A) of the hemisphere can be calculated as:
A = 2πr^2
A = 2π(10ft)^2
A = 200π square feet
3. Total surface area:
To find the total surface area, we need to add the surface area of the cylinder and the hemisphere.
Total surface area = Surface area of the cylinder + Surface area of the hemisphere
Total surface area = 1200π + 200π
Total surface area = 1400π square feet
Therefore, the surface area of the right circular cylinder topped with a hemisphere is 1400π square feet.
To calculate the surface area of a right circular cylinder topped with a hemisphere, you need to find the surface area of the cylinder and add the surface area of the hemisphere.
Step 1: Calculate the surface area of the cylinder:
The surface area of a cylinder is given by the formula:
A_cylinder = 2πr_cylinder * h_cylinder,
where r_cylinder is the radius of the cylinder's base and h_cylinder is the height of the cylinder.
Since the cylinder is right circular, the base of the cylinder is a circle. The radius of the base is half of the length of the cylinder, so r_cylinder = 20ft / 2 = 10ft. The height of the cylinder is given as 60ft.
Therefore, the surface area of the cylinder is:
A_cylinder = 2 * π * 10ft * 60ft.
Step 2: Calculate the surface area of the hemisphere:
The surface area of a hemisphere is given by the formula:
A_hemisphere = 2πr_hemisphere^2,
where r_hemisphere is the radius of the hemisphere.
Since the hemisphere is that of the cylinder's top, the radius of the hemisphere is the same as the radius of the cylinder's base, so r_hemisphere = 10ft.
Therefore, the surface area of the hemisphere is:
A_hemisphere = 2 * π * (10ft)^2.
Step 3: Calculate the total surface area:
To find the total surface area, add the surface area of the cylinder and the surface area of the hemisphere:
Total Surface Area = A_cylinder + A_hemisphere.
Now, you can substitute the values into the equation and calculate the result.