SURFACE AREAS AND VOLUMES
Frequently Asked Questions
The total area covered by the surfaces of a 3D solid.
The area of only the curved part of a solid.
The sum of all faces (curved + flat) of a solid.
The space occupied by a solid measured in cubic units.
To find materials needed to cover an object like paint or wrapping.
To find capacity, such as water tanks and containers.
Surface area \(\Rightarrow cm^2,\ m^2;\ Volume \Rightarrow cm^3,\ m^3\).
TSA = 2(lb + bh + hl).
Volume = l × b × h.
TSA = \(6a^2\).
Volume = \(a^3\).
CSA \(= 2\pi rh\).
TSA \(= 2\pi r(r + h)\).
Volume = \(\pi r^2h\).
\( l = \sqrt{r^{2} + h^{2}} \).
CSA = \(\pi rl\).
TSA \(= \pi r(r + l)\).
Volume = \( \frac{1}{3}\pi r^{2} h \).
TSA = \(4\pi r^2\).
Volume = \( \frac{4}{3}\pi r^{3} \).
CSA = \(2\pi r^2\\\) TSA = \(3\pi r^2\).
Volume = \( \frac{2}{3}\pi r^{3} \).
Add or subtract exposed areas depending on joining or removal.
Add volumes if joined; subtract if a part is removed (hole, cavity).
Painting, wrapping, building, manufacturing.
Water tanks, packaging, measuring capacity.
Divide by \(10^{6}\).
Multiply by \(10^{4}\).
Because radius is squared and cubed in formulas.
CSA doubles.
Volume becomes 8 times.
Surface area becomes 9 times.
They store more volume using less material.
Spheres distribute pressure uniformly.
CSA = 2 × \(\pi\) × 7 × 10 = 440 cm² (approx).
Volume = 125 cm³.
TSA = 154 cm².
CSA \(\Rightarrow\) curved part; TSA \(\Rightarrow\) all surfaces.
TSA/CSA of cylinder and volume of cone.
Identify radius/diameter correctly and check exposed surfaces.
Three identical cones fill one cylinder of same base and height.
Shape may have small surface area but large volume.
r, h, l form a right triangle in a cone.
Yes, because TSA = CSA + base areas.
No, it is \( \frac{2}{3} \) of sphere.
Chart paper, cardboard, thermocol.
To visualize and construct TSA/CSA easily.
Rearrange formula for required variable.
Use 22/7 when multiples of 7 are present; otherwise 3.14.
Composite solids and multi-step TSA/volume problems.
