The total surface area of the cylinder is approximately 967.4 cm², rounded to one decimal place.
How to find the total surface area of a cylinder
To find the total surface area of a cylinder, calculate the sum of the areas of the two bases and the lateral surface area.
The formula for the lateral surface area of a cylinder is given by:
Lateral surface area = 2πrh, where r is the radius and h is the height.
The formula for the area of a circle (base of the cylinder) is:
Base area = πr², where r is the radius.
Given:
Radius (r) = 7 cm
Height (h) = 15 cm
Calculating the lateral surface area:
Lateral surface area = 2πrh = 2π(7 cm)(15 cm)
Calculating the base area:
Base area = πr² = π(7 cm)²
To find the total surface area, add the lateral surface area and twice the base area:
Total surface area = Lateral surface area + 2(Base area)
Now, calculate each component:
Lateral surface area = 2π(7 cm)(15 cm)
Base area = π(7 cm)²
Total surface area = 2π(7 cm)(15 cm) + 2[π(7 cm)²]
Calculating the total surface area:
Total surface area = 2π(7 cm)(15 cm) + 2[π(7 cm)²]
Total surface area = 210π cm² + 98π cm²
Now, approximate the total surface area by substituting the value of π as approximately 3.14159:
Total surface area ≈ 210π cm² + 98π cm²
Total surface area ≈ 308π cm²
Approximating further:
Total surface area ≈ 308(3.14159) cm²
Total surface area ≈ 967.38972 cm²
Therefore, the total surface area of the cylinder is approximately 967.4 cm², rounded to one decimal place.