Prisms, cylinders, cones, pyramids and spheres: volume, surface area, capacity in litres and compound solids.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
How much water does a tank hold? How much paint covers a cone? These are the “3-D” questions — and every formula you need is on the exam sheet except the sphere and cone surface areas.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Choose a solid, change its size, fold a net, and compare similar solids.
Copy these into your notebook in your own words — that is how they stick.
V = Ah (cross-section area × length). Cube: V = s³, SA = 6s².
V = lwh; SA = 2(lw + lh + wh).
V = πr²h; curved SA = 2πrh; total SA = 2πr² + 2πrh.
V = ⅓πr²h; curved SA = πrl; l² = r² + h²; total SA = πr² + πrl.
V = ⅓ × base area × h.
V = 4/3 πr³; SA = 4πr². Hemisphere: V = ⅔πr³; total SA = 3πr².
1 cm³ = 1 mL; 1 000 cm³ = 1 L; 1 m³ = 1 000 L.
The exam list gives V for prism, cylinder, pyramid; the sphere and cone volume, and all surface areas, you must know.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (18 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
A water tank is a cylinder of radius 70 cm and height 120 cm. Use π = 22/7.
(a) Calculate the volume of the tank in cm³. [3]
(b) Express the capacity of the tank in litres. [1]
(c) The tank is three-quarters full. How many litres of water does it contain? [2]
(d) Calculate the curved surface area of the tank in m², to 2 decimal places. [3]
Question 2 [9 marks]
An ice-cream cone is a cone of radius 3 cm and vertical height 8 cm with a hemisphere of radius 3 cm on top. Use π = 3.14.
(a) Calculate the volume of the cone. [2]
(b) Calculate the volume of the hemisphere. [2]
(c) Hence find the total volume of ice cream if the cone is filled and the hemisphere is added. [1]
(d) Calculate the slant height of the cone and the curved surface area of the cone, to 1 decimal place. [4]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.