Class 10 • Maths • Chapter 12
SURFACE AREAS AND VOLUMES
True & False Quiz
Solid. Surface. Volume.
✓True
✗False
25
Questions
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Ch.12
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Class
Why True & False for SURFACE AREAS AND VOLUMES?
How this format sharpens your conceptual clarity
🔵 Surface Areas and Volumes describe the physical world — packaging, construction, and manufacturing all depend on these calculations.
✅ T/F targets formula confusion between CSA, TSA, and Volume — and the conversion of solids (e.g., cone into sphere).
🎯 For a cone, l² = r² + h² (slant height formula) — frequently appears as a true/false premise.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The total surface area of a cube of edge \(a\) is \(6a^{2}\).
Q 2
The volume of a cube of edge \(a\) is \(6a^{3}\).
Q 3
The volume of a cuboid of length \(l\), breadth \(b\) and height \(h\) is \(lbh\).
Q 4
The total surface area of a cuboid is \(2(lb+bh+hl)\).
Q 5
The curved surface area of a right circular cylinder of radius \(r\) and height hhh is \(2\pi rh\).
Q 6
The total surface area of a right circular cylinder is \(2\pi rh\) only.
Q 7
The volume of a right circular cylinder of radius \(r\) and height \(h\) is \(\pi r^{2}h\).
Q 8
The curved surface area of a right circular cone is \(\pi rl\), where \(l\) is the slant height.
Q 9
The total surface area of a right circular cone is \(\pi rl\) only.
Q 10
The volume of a right circular cone of radius \(r\) and height \(h\) is \(\frac{1}{2}\pi r^{2}h\).
Q 11
The total surface area of a sphere of radius \(r\) is \(4\pi r^{2}\).
Q 12
The volume of a sphere of radius \(r\) is \(\frac{4}{3}\pi r^{3}\).
Q 13
The volume of a hemisphere of radius \(r\) is \(\frac{2}{3}\pi r^{3}\).
Q 14
The curved surface area of a hemisphere of radius \(r\) is \(2\pi r^{2}\).
Q 15
The total surface area of a closed hemisphere (including its circular base) of radius \(r\) is \(3\pi r^{2}\).
Q 16
When a solid is melted and recast into another shape without loss of material, its total volume remains unchanged.
Q 17
If a solid sphere is melted and formed into a cylinder, the volume of the sphere must equal the volume of the cylinder (ignoring wastage).
Q 18
Surface area is measured in cubic units and volume in square units.
Q 19
If the radius of a sphere is doubled, its volume becomes four times the original volume.
Q 20
If the height of a cylinder is tripled while keeping the radius same, its volume is also tripled.
Q 21
For a right circular cone, the slant height is always less than the vertical height.
Q 22
For any solid, if every linear dimension is scaled by a factor kkk, then its surface area is multiplied by \(k^{2}\).
Q 23
For any solid, if every linear dimension is scaled by a factor kkk, then its volume is multiplied by \(k^{3}\).
Q 24
The capacity of a container (like a tank or bottle) is numerically equal to its surface area.
Q 25
In real-life questions about painting walls or wrapping objects, the relevant measure is usually surface area, not volume.
Key Takeaways — SURFACE AREAS AND VOLUMES
Core facts for CBSE Boards & exams
1
Cylinder: CSA = 2πrh; TSA = 2πr(h+r); V = πr²h.
2
Cone: CSA = πrl; TSA = πr(l+r); V = ⅓πr²h; l² = r²+h².
3
Sphere: SA = 4πr²; V = (4/3)πr³.
4
Hemisphere: CSA = 2πr²; TSA = 3πr²; V = (2/3)πr³.
5
Frustum: CSA = π(r₁+r₂)l; V = (πh/3)(r₁²+r₂²+r₁r₂); l² = h²+(r₁−r₂)².
6
When a solid is melted and recast, the VOLUME is conserved, not the surface area.