Question
15 cm 5 cm find the surface area of the cylinder below use the approximation 3.14 for pi
Answers
Answered by
GPT 3.5
To find the surface area of a cylinder, we need to calculate the areas of the two circular bases and the lateral surface.
1. Base Area: The area of a circle is given by the formula A = πr^2, where r is the radius. The radius of each base is half the diameter, so for the first base:
radius 1 = 15 cm / 2 = 7.5 cm
Area of base 1 = π(7.5 cm)^2 = 56.25π cm^2
For the second base, which has the same dimensions:
radius 2 = 7.5 cm
Area of base 2 = π(7.5 cm)^2 = 56.25π cm^2
2. Lateral Surface Area: The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Since the cylindrical body is formed from the length of the rectangle, the height is 5 cm. Using radius 1:
Area of lateral surface = 2π(7.5 cm)(5 cm) = 75π cm^2
3. Total Surface Area: To find the total surface area, we sum the areas of the bases and the lateral surface:
Total surface area = Area of base 1 + Area of base 2 + Area of lateral surface
= 56.25π cm^2 + 56.25π cm^2 + 75π cm^2
= 187.5π cm^2
Using the approximation π ≈ 3.14:
Total surface area ≈ 187.5(3.14) cm^2
≈ 588.75 cm^2
Therefore, the surface area of the given cylinder is approximately 588.75 cm^2.
1. Base Area: The area of a circle is given by the formula A = πr^2, where r is the radius. The radius of each base is half the diameter, so for the first base:
radius 1 = 15 cm / 2 = 7.5 cm
Area of base 1 = π(7.5 cm)^2 = 56.25π cm^2
For the second base, which has the same dimensions:
radius 2 = 7.5 cm
Area of base 2 = π(7.5 cm)^2 = 56.25π cm^2
2. Lateral Surface Area: The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius and h is the height. Since the cylindrical body is formed from the length of the rectangle, the height is 5 cm. Using radius 1:
Area of lateral surface = 2π(7.5 cm)(5 cm) = 75π cm^2
3. Total Surface Area: To find the total surface area, we sum the areas of the bases and the lateral surface:
Total surface area = Area of base 1 + Area of base 2 + Area of lateral surface
= 56.25π cm^2 + 56.25π cm^2 + 75π cm^2
= 187.5π cm^2
Using the approximation π ≈ 3.14:
Total surface area ≈ 187.5(3.14) cm^2
≈ 588.75 cm^2
Therefore, the surface area of the given cylinder is approximately 588.75 cm^2.