Find the total surface area of a hollow cylinder with an inner radius of 7cm , outer radius 14cm and a height of 30cm
The formula for the total surface area of a hollow cylinder is given by:
A = 2π(r₁+r₂)h + 2π(r₂² - r₁²)
Given:
Inner radius (r₁) = 7 cm
Outer radius (r₂) = 14 cm
Height (h) = 30 cm
Using these values in the formula, we can calculate the total surface area of the hollow cylinder:
A = 2π(7 + 14)30 + 2π(14² - 7²)
A = 2π(21)30 + 2π(196 - 49)
A = 2π(21)30 + 2π(147)
A = 1260π + 294π
A ≈ 1554π
Therefore, the approximate total surface area of the hollow cylinder is 1554π square centimeters.
To find the total surface area of a hollow cylinder, you need to calculate the surface area of the outer curved surface and subtract the surface area of the inner curved surface.
1. Surface area of the outer curved surface:
The outer curved surface of the hollow cylinder consists of two circular bases and a lateral surface. The formula to calculate the lateral surface area of a cylinder is given by 2πrh, where r is the radius and h is the height. Since we need to calculate the surface area of only the curved part, we exclude the area of the bases and consider the height as the slant height.
Outer surface area = 2π × outer radius × height
= 2π × 14 cm × 30 cm
= 840π cm² (approx. 2645.55 cm²)
2. Surface area of the inner curved surface:
The inner curved surface of the hollow cylinder also consists of two circular bases and a lateral surface. Using the same formula as above, we will calculate the lateral surface area using the inner radius as the radius.
Inner surface area = 2π × inner radius × height
= 2π × 7 cm × 30 cm
= 420π cm² (approx. 1318.31 cm²)
3. Calculate the total surface area:
Total surface area = Outer surface area - Inner surface area
= 840π cm² - 420π cm²
= 420π cm² (approx. 1317.24 cm²)
Therefore, the total surface area of the given hollow cylinder is approximately 1317.24 cm².