Mensuration — Class 10 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Mensuration, written for Class 10 Maharashtra SSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Mensuration in one look
surface area and volume of the standard solids, and what happens when they are combined or melted down
Two different questions the words are asking
- volume is the space filled inside a solid, measured in cubic units such as cm³ or m³
- surface area is the skin of the solid, measured in square units such as cm² or m²
- curved surface area counts only the rounded part, leaving out any flat circular ends
- total surface area counts the curved part plus every flat face the solid actually has
- the words in the question decide which: painting or covering wants area, while filling, holding or melting wants volume
- a solid open at the top, such as a bucket or a pipe, does not include that face in its total surface area
Cylinder, cone and sphere
- cylinder, curved surface then total
2π rh,quad 2π r(h + r) - cylinder, volume
V = π r^2 h - cone, curved surface then total
π rl,quad π r(l + r) - cone, volume, one third of the cylinder
V = 1/3π r^2 h - sphere, surface area then volume
4π r^2,quad 4/3π r^3 - hemisphere, curved then total, then volume
2π r^2,quad 3π r^2,quad 2/3π r^3
The slant height, which the cone formulas need
- a cone has three lengths: the radius r, the vertical height h and the slant height l
- they form a right angled triangle, so l^2 = r^2 + h^2
- the area formulas use l, while the volume formula uses h, and that is the distinction most often missed
- a question that gives r and h and asks for surface area wants the Pythagoras step first
- a question that gives r and l and asks for volume needs h recovered as h = √l^2 - r^2
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Mensuration sheet covers
- Surface area
- Volume
- Two different questions the words are asking
- Cylinder, cone and sphere
- cylinder, curved surface then total
- cylinder, volume
- cone, curved surface then total
- cone, volume, one third of the cylinder
- sphere, surface area then volume
- hemisphere, curved then total, then volume
- The slant height, which the cone formulas need
- A cone needing the slant height first
- Conversion of solids
- Melting and recasting
- Melting, recasting and pouring
- A melting problem end to end
- Combined solids, and which faces disappear
- Area of a sector
- Length of an arc
- The sector and the arc
- Which formula the wording is asking for
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Mensuration the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.