Volume and surface area – Grade 10 math lesson
Lesson 8 of 16 in the Grade 10 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 10 (ages 15–16) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 10 (ages 15–16)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Can two shapes have the same volume but different surface areas?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Mixing up volume and surface area units. Volume: cm³. Area: cm².
- Missing hidden faces in surface area. Draw the net and label every face.
Tip for home: Work out how much a tin or a fish tank holds.
What your child will learn
Learning goal: find the volume and surface area of prisms, cylinders, cones and spheres.
Success looks like
- I can find the volume of prisms and cylinders.
- I can find surface areas.
- I can use the formulas for cones and spheres.
Key words
- volume
- space inside a solid (cubic units)
- surface area
- total area of all the faces (square units)
- prism
- a solid with the same cross-section all along
- cross-section
- the shape you see when you slice across
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Find the volume of a tin or a cereal box by measuring, then check with water or rice.
The big ideas (for the adult)
The volume of a prism is the area of its cross-section × its length. A cylinder is a prism with a circle cross-section: πr²h.
Surface area is the total area of all the faces. Sketch the net to make sure no face is missed.
Cones and spheres have their own formulas: cone volume = ⅓πr²h; sphere volume = ⁴⁄₃πr³. Density = mass ÷ volume links volume to mass.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 10 math lessons
- Factoring
- Quadratic equations
- Identities and proof
- Functions
- Graphing functions
- Exponential functions
- Circles: circumference and area
- The Pythagorean theorem
- Right triangle trigonometry
- Transformations
- Similarity and congruence
- Properties of quadrilaterals
- Coordinate geometry
- Cross sections of 3-D figures
- Geometric constructions
Curriculum
Common Core State Standards HSG.GMD.A.3: “Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*”
Common Core State Standards HSG.MG.A.1: “Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.