CBSE Class 10 Mathematics Chapter 12 Surface Areas and Volumes — 20 MCQs with Answers

Combinations of solids involve joining two or more basic three-dimensional shapes such as a hemisphere atop a cylinder, a cone mounted on a cylinder, or a cylinder with hemispherical ends. Surface area calculations require care: the base of the hemisphere and the top of the cylinder coincide, so that circular area is not counted twice. Volume is simply the sum of individual volumes. The 2024 CBSE Class 10 board paper carried a 5-mark question on a rocket shape (cone on cylinder on cylinder), asking for total surface area and volume. Understanding which surfaces are exposed and which are hidden is the key skill. NCERT Exercise 13.1 (renumbered 12.1 in some editions) introduces these beautifully with solved examples. Practice these MCQs to cement formula selection and substitution under time pressure.

A frustum of a cone is obtained by slicing a cone with a plane parallel to its base and removing the smaller cone from the top. It has two circular bases of radii r₁ (top, smaller) and r₂ (bottom, larger), and height h. The NCERT formulas are: Curved Surface Area = π(r₁ + r₂)l where l is slant height √(h² + (r₂ − r₁)²); Total Surface Area = π(r₁ + r₂)l + πr₁² + πr₂²; Volume = (1/3)πh(r₁² + r₂² + r₁r₂). Real-world objects like buckets, lamp shades, and funnels are modeled as frustums. The 2023 CBSE board paper asked a 3-mark question on the volume of a frustum-shaped water tank. Substitution errors — especially confusing r₁ and r₂ — cost marks. These MCQs drill correct identification and formula use.

Conversion problems state that a solid of one shape is melted and recast (without loss) into another shape, so volumes are equal but surface areas differ. Common conversions: sphere to cylinder, cone to sphere, cylinder to cones. The key principle is Volume₁ = Volume₂. If n identical objects are formed, then n × Volume(each new object) = Volume(original object). The 2024 CBSE sample paper included a 2-mark MCQ where a solid sphere of radius 6 cm is melted into 27 smaller spheres; find radius of each. Answer: (6³)/27 = r³, so r = 2 cm. Unit consistency is vital: if diameter is given, halve it to get radius; if volume is in litres, convert to cm³ (1 litre = 1000 cm³). These MCQs sharpen algebraic manipulation and formula recall for volume of sphere, cylinder, cone, and hemisphere.

Assertion-Reason (A-R) questions have appeared in CBSE Class 10 Mathematics papers since 2021. Each A-R MCQ presents two statements: Assertion (A) and Reason (R). You must decide if both are true, and if R correctly explains A. The four standard options are: (A) Both A and R are true and R is the correct explanation of A; (B) Both A and R are true but R is not the correct explanation of A; (C) A is true but R is false; (D) A is false but R is true. In Surface Areas and Volumes, A-R questions often link formula derivation to dimensional analysis or test whether a property (like 'doubling radius quadruples area') is correctly justified. Read both statements carefully before choosing. These MCQs reward conceptual depth over rote memorization and typically carry 1 mark each in Section A of the board paper.

Higher Order Thinking Skills (HOTS) MCQs go beyond direct formula substitution. They may present a real-world scenario — like optimizing the design of a water tank, comparing costs of materials for different shapes, or finding dimensions given constraints on volume and surface area. The CBSE marking scheme awards these questions to test analytical ability and problem-solving. For instance, a HOTS MCQ might give the cost per square metre of canvas and ask which tent shape (conical vs cylindrical with hemispherical top) is cheaper for a fixed volume. Such questions require setting up equations, eliminating variables, and interpreting results. Practice these to build confidence for the 3-mark and 5-mark application problems in Sections C and D of the board paper, which often mirror MCQ logic but demand full working.

CBSE MCQ setters design distractors (wrong options) that catch common errors. For Surface Areas and Volumes, typical traps include: using diameter instead of radius (inflates answer by factor of 4 in area, 8 in volume); forgetting to subtract the common base area in combinations; confusing slant height with vertical height; adding volumes when asked for surface area (or vice versa); and unit mismatches (answer in cm² when options are in m²). Another frequent error is taking π = 3.14 when the question specifies π = 22/7, or vice versa. In frustum problems, swapping r₁ and r₂ yields a wrong but plausible answer. Always write down the formula first, identify given values with labels, substitute carefully, and check units. Elimination strategy helps: if your computed answer does not match any option, recheck calculation before guessing. Practicing 50+ MCQs builds pattern recognition for these traps.

Section A of the CBSE Class 10 Mathematics paper contains 20 MCQs of 1 mark each, covering all chapters. Surface Areas and Volumes typically contributes 2-3 MCQs. Time management is crucial: aim to solve all 20 MCQs in 20-25 minutes, leaving 2.5-3 hours for subjective sections. Read each question twice to avoid misreading 'diameter' as 'radius' or 'volume' as 'surface area'. Write the formula in the margin if allowed, then substitute. If calculation is lengthy, check whether options are far apart — you might estimate. For Assertion-Reason, evaluate A and R independently first, then check logical connection. If stuck, mark a guess (no negative marking in CBSE) and move on; return if time permits. In numerical MCQs, back-substitution can verify: plug your chosen answer back into the condition. CBSETUTOR.ai offers adaptive MCQ practice with instant photo-upload solving and step-by-step hints at ₹999/month (one price for Classes 6-12, 3-day free trial). Students report saving 30-40 minutes per paper through timed MCQ drills and formula-flash modules on the platform.