Need to Know

Volume & Surface Area

The mensuration formulas you must have ready for the exam.

How to use this: read each heading and say the formula in your head first, then tap Show me to check.

The box

2 rules

Rule 01

Volume of a box

V = ℓ × b × h

Rule 02

Surface area

Closed box: A = 2(ℓb + bh + ℓh)

Open-top: drop one ℓb face.

2 rules

Rule 03

Volume of a cylinder

V = πr²h

Rule 04

Surface area

Curved part: 2πrh. Closed cylinder: 2πrh + 2πr².

2 rules

Rule 05

Volume of a sphere

V = 43πr³

Rule 06

Surface area

A = 4πr²

1 rule

Rule 07

Volume of a cone

V = 13πr²h — a third of the matching cylinder.

3 rules

Rule 08

Units matter

Area is measured in cm²; volume in cm³. Always write the units.

Rule 09

Working backwards

Given the volume or area, substitute it into the formula and solve for the missing length.

Rule 10

Space problems

Empty space = container volume − volume of the solids inside. Then percentage if asked.

Mathslive.ie · Volume & Surface Area · Need to Know