• The volume of a 3D shape is the amount of fillable space on the inside.
• Volume is measured in cubic units (units ³).
• The surface area of a 3D shape is the amount of coverable space on the outside.
• Surface Area is measured in square units (units ²).

Here’s how to calculate the volume and surface area of a cylinder:
EXAMPLE: Find the volume and surface area of the cylinder below.

VOLUME:
The formula for the volume of a cylinder is:
Volume = πr²h

• r is the radius of the circle
• h is the height of the cylinder.

In our figure, the height is 10 cm.
We need the radius, but we’re given the diameter (7 cm).
To calculate the radius, just cut the diameter in half.
So, r = 3.5 cm
All we need to do now is substitute the values into our formula.

V= πr²h
V = π(3.5 cm)²(10 cm)
V = π(12.25 cm²)(10 cm)
V = π(122.5 cm³)
V = 122.5π cm³ OR V ≈ 384.9 cm³

SURFACE AREA:
To find the surface area of the entire figure, find the area of each face.

Note: The two bases are both circles, so we’ll use A = πr² for those.
To find the area of the side, imagine cutting straight up the side of the cylinder and laying it flat. You would end up with a rectangle.
The height of the rectangle would be 10 cm, and the length of the rectangle would be equal to the circumference of the circular base.
That means that the area of the curved side of the cylinder would be length times height, or in this case : (2πr) times height.

Area of bottom = πr² = π(3.5 cm)² = π(12.25 cm²) = 12.25π cm²
Area of the top = πr² = π(3.5 cm)² = π(12.25 cm²) = 12.25π cm²
Area of the curved side = 2πrh = 2π(3.5 cm)(10 cm) = 2π(35 cm²) = 70πcm²

Surface area = The sum of the areas of all 3 faces
SA = 12.25π cm² + 12.25π cm² + 70πcm²
SA = 24.5π cm² + 70π cm²
SA = 94.5π cm² OR SA ≈ 296.9 cm²