Surface areas and volumes:
The chapter 'Surface areas and volumes' is typically carries a weightage of around 6 marks in the board exam. it covers the concepts like surface area of combined solids and volume of combined solids.
Most possible variation of question type that we can expect in board exams as per previous year question paper are discussed below:
| Total Marks 6 | |
| Variation 1 | Variation 2 |
Total marks = 6
|
Total marks = 6
|
- Surface area of combined solids - Curved surface area and total surface area of combined solids
- Volume of combined solids - Volume of combined solids
| Important Concpet(Learning Outcomes) | Expected Question Type | Concept dealt with |
| Surface area of combined solids |
|
|
| Surface area of combined solids | Sec C, Sec D, Sec E | |
| Volume of combined solids | Sec A, Sec B | |
| Volume of combined solids | Sec C, Sec D |
Let us recall the concepts in Surface areas and volumes:
| SOLID | TOTAL SURFACE AREA | CURVED SURFACE AREA | VOLUME |
| Cube | \(6a^2\) | \(4a^2\) | \(a^3\) |
| Cuboid | \(2(lb+bh+hl)\) | \(2h(l+b)\) | \(lbh\) |
| Cone | \(\pi r(l+r)\) | \(\pi rl\) | \(\frac{1}{3}\pi r^2h\) |
| Cylinder | \(2\pi r(h+r)\) | \(2\pi rh\) | \(\pi r^2h\) |
| Sphere | \(4\pi r^2\) | \(4\pi r^2\) | \(\frac{4}{3}\pi r^3\) |
| Hemisphere | \(3\pi r^2\) | \(2\pi r^2\) | \(\frac{2}{3}\pi r^3\) |
Common mistakes to avoid:
1. Radius conversion: Always have the diameter to radius in the very first line of your calculation to avoid using raw diameter in \(r\) based formulas.
2. For cone, always verify whether vertical height or a slant height is given.
3. For combined solids, count only the surfaces that are exposed/visible when finding the total surface area.
4. Draw or visualize the solid before choosing the formula, identify which parts are added or removed.
5. Remove the area of the common face that gets covered. Count only curved surfaces and any outer flat faces that remain visible.
6. When two or more solids are joined together, add their individual volumes to find the total volume.
7. When a part is cut out or hollwed, subtract its volume from the original solid.
Exam tips & tricks:
1. Memorize and understand the above given formulas.
2. Identify the solid(s), decide whether it is a combined solid or cavity, determine whether CSA, TSA or volume is required, identify exposed/hidden surfaces or removed parts, check radius and height, and use the given value of \(