Surface Area of 3D Shapes
Grade 5What surface area means
Surface area is the total area of all the faces of a 3D shape. Think of it as the amount of wrapping paper needed to cover the shape exactly, with no overlap.
For most shapes you list and add each face. For curved surfaces, use the relevant formula.
Cylinder: SA = 2πr² + 2πrh (two circles + curved band)
Cone: SA = πr² + πrl (base circle + curved surface, l = slant height)
Sphere: SA = 4πr²
Slant height of a cone
The slant height l is the distance along the surface from the base edge to the apex — not the vertical height. Find it with Pythagoras: l = √(r² + h²).
Surface area questions sometimes give you the vertical height instead of the slant height. Use Pythagoras to find the slant height first, then use πrl.
Worked example
EXAMPLE
A cylinder has radius 4 cm and height 9 cm. Find the total surface area. Give your answer to 3 significant figures.
Two circular ends: 2 × π × 4² = 2 × 16π = 32π cm². Curved surface: 2π × 4 × 9 = 72π cm². Total = 32π + 72π = 104π ≈ 327 cm² (to 3 s.f.).
Try this one
A solid sphere has a radius of \( 3 \) cm.
Calculate the volume of the sphere. Give your answer to \( 1 \) decimal place. [3]
Nova's hint:
Try to Solve it with Nova?
Use the sphere volume formula, which involves the cube of the radius.
Ask yourself: 'have I cubed the radius rather than squaring it?' Work out \( r^3 \) first, then apply the \( \dfrac{4}{3}\pi \) factor.
