Module 5 · Mensuration
Chapter 51: Volume Applications
Mensuration
3 topics
What this chapter covers
The 3 topics below make up Volume Applications on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Volumes & surface areas of standard solids
| Cylinder | V = πr²h ; CSA = 2πrh ; TSA = 2πr(r + h) |
|---|---|
| Cone | V = (1/3)πr²h ; CSA = πrl ; l = √(r² + h²) |
| Sphere | V = (4/3)πr³ ; surface area = 4πr² |
| Hemisphere | V = (2/3)πr³ ; CSA = 2πr² ; TSA = 3πr² |
| Cube / cuboid | V = a³ or l×b×h ; cuboid TSA = 2(lb + bh + hl) |
Conservation power-tools
| Recast one solid into another | V(old) = V(new) ⇒ equate and solve |
|---|---|
| Recast into n equal pieces | V(big) = n × V(small) |
| Level rise from immersed solid | A(base) × Δh = V(object) ⇒ Δh = V/A |
| Water poured between vessels | V is fixed: A₁h₁ = A₂h₂ |
| Combined-solid surface area | add CSAs; never double-count a shared circular face |
CAT reference
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