Surface Area of a Cylinder Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A cylindrical can has a total surface area of 150π150\pi cm² and a radius of 5 cm. Find the height.

Solution

  1. 1
    Step 1: Use SA=2πr2+2πrhSA = 2\pi r^2 + 2\pi rh with SA=150πSA = 150\pi and r=5r = 5.
  2. 2
    Step 2: 150π=2π(5)2+2π(5)h=50π+10πh150\pi = 2\pi(5)^2 + 2\pi(5)h = 50\pi + 10\pi h.
  3. 3
    Step 3: Subtract 50π50\pi: 100π=10πh100\pi = 10\pi h.
  4. 4
    Step 4: Divide by 10π10\pi: h=10h = 10 cm.

Answer

The height is 1010 cm.
To find the height from the surface area, substitute the known values and solve for hh. The 2πr22\pi r^2 term accounts for the fixed area of the two bases, and the remaining surface area (SA−2πr2SA - 2\pi r^2) divided by 2πr2\pi r gives the height.

About Surface Area of a Cylinder

The total area of the surface of a cylinder, consisting of two circular bases and a rectangular lateral surface that wraps around.

Learn more about Surface Area of a Cylinder →

More Surface Area of a Cylinder Examples

Example 1 easy

A cylinder has radius 5 cm and height 8 cm. Find its total surface area. Leave your answer in terms

Example 3 medium

Find the total surface area of a cylinder with radius 4 cm and height 10 cm.

Example 4 easy

Find the lateral surface area only (not the bases) of a cylinder with radius 3 cm and height 7 cm. L

Example 5 hard

A cylinder's height equals its diameter. If the total surface area is [formula] cm², find the radius

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