find the surface area of the cylinder in terms of pi. A cylinder is shown. Its diameter is labeled 14 centimeters and its height is labeled 18 centimeters. can anyone plz help im stuck!
Yes, I can help you.
The formula to find the surface area of a cylinder is:
SA = 2πr² + 2πrh
where r is the radius of the cylinder and h is its height.
We are given the diameter of the cylinder, which is 14 cm. To find the radius, we need to divide the diameter by 2:
r = d/2 = 14/2 = 7 cm
Now we can substitute the values of r and h into the formula:
SA = 2π(7)² + 2π(7)(18)
SA = 2π(49) + 2π(126)
SA = 98π + 252π
SA = 350π
So the surface area of the cylinder in terms of pi is 350π square centimeters.
omg thankyou so much!!
To find the surface area of a cylinder in terms of pi, you need to calculate the sum of the areas of its base and lateral surface.
1. The base of the cylinder is a circle, and its area can be calculated using the formula A = πr^2, where r is the radius.
- The diameter of the cylinder is given as 14 centimeters, so the radius is half of that, which is 14/2 = 7 centimeters.
- Therefore, the area of the base is A_base = π * (7 cm)^2.
2. The lateral surface of the cylinder is a rectangle that wraps around the base. Its area can be calculated using the formula A = 2πrh, where r is the radius and h is the height.
- We already have the radius as 7 centimeters, and the height is given as 18 centimeters.
- Therefore, the area of the lateral surface is A_lateral = 2π * (7 cm) * (18 cm).
3. To find the total surface area, sum the areas of the base and the lateral surface:
- Total Surface Area = A_base + A_lateral
= π * (7 cm)^2 + 2π * (7 cm) * (18 cm)
= π * 49 cm^2 + 2π * 126 cm^2.
So, the surface area of the given cylinder in terms of pi is π * 49 cm^2 + 2π * 126 cm^2.
To find the surface area of a cylinder in terms of pi, we need to calculate the sum of the areas of its two bases and its curved surface.
1. The area of each base of the cylinder is given by the formula A = πr^2, where r is the radius.
- The diameter of the cylinder is given as 14 centimeters, so the radius (r) is half of the diameter, which is 7 centimeters.
- Therefore, the area of each base is A = π(7 cm)^2.
2. The curved surface area of the cylinder is given by the formula A = 2πrh, where r is the radius and h is the height of the cylinder.
- We already have the value for the radius (r = 7 cm) and the height (h = 18 cm).
- Therefore, the curved surface area is A = 2π(7 cm)(18 cm).
3. To find the total surface area, we sum the areas of the bases and the curved surface area.
- Total Surface Area = 2(Base Area) + Curved Surface Area
Now we can calculate the surface area of the cylinder in terms of pi:
Base Area = π(7 cm)^2 = 49π cm^2
Curved Surface Area = 2π(7 cm)(18 cm) = 252π cm^2 (rounded to the nearest whole number)
Total Surface Area = 2(49π cm^2) + 252π cm^2 = 350π cm^2
Therefore, the surface area of the given cylinder, in terms of pi, is 350π square centimeters.