What is the surface area of a cylinder with a top area of 35pi and a height of 20cm
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Is it 1972.243
To find the surface area of a cylinder, we need to calculate the sum of the areas of the curved surface and the top and bottom circles.
The curved surface area of a cylinder is given by the formula: A_curved = 2πrh, where π is a mathematical constant (approximately 3.14), r is the radius of the cylinder, and h is the height of the cylinder.
Given the height of the cylinder, which is 20 cm, we can assume that the curved surface area is the same as the given top area, 35π cm². Therefore, we need to find the radius of the cylinder.
The top area of the cylinder is equal to the area of the circle, which is given by the formula: A_circle = πr², where r is the radius of the circle.
We can rearrange this equation to solve for the radius: r = √(A_circle / π).
In this case, the top area of the cylinder is 35π cm². Substituting this value into the equation, we have: r = √(35π / π) = √35 ≈ 5.92 cm.
Now that we have the radius, we can calculate the curved surface area: A_curved = 2πrh = 2π(5.92 cm)(20 cm) = 236.8π cm².
Finally, we add the area of the curved surface to the areas of the top and bottom circles to find the total surface area of the cylinder: A_total = A_curved + 2A_circle = 236.8π + 2(35π) = 236.8π + 70π = 306.8π cm².
So, the surface area of the cylinder is approximately 306.8π cm².