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Mensuration (Area & Volume) Practice Questions with Detailed Solutions – Level 2

Medium-level mensuration practice on solids: recasting spheres and cones, frustum capacity, water-level rise, percentage change in volume and surface area, and painting costs, with worked solutions.

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Questions, answer key and solutions.

Questions
50
Duration
60 min
Marks
50

Negative marking

Attempts
100
Access
Free
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Normal practice, or a Simulated test

Both use the same questions. Normal practice is untimed and needs no account: choose an option and the answer and solution appear at once. The Simulated test is the real computer-based format, with one 60-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

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Every question on one page, loading as you scroll. Choose an option and see straight away whether it was right.

  • No timer. Nothing to start and nothing to submit. Stop whenever you like.
  • Answered as you choose. Tap an option and it is marked at once, with the correct answer shown.
  • Solutions in place. The explanation, and the video where one has been added, sit under the question.
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Real exam conditions

Simulated

Timed CBT

The computer-based test format: one clock, a question palette, and a score the moment you submit.

  • A clock that does not pause. 60 minutes from the moment you begin, and the paper is submitted for you when it reaches zero.
  • Question palette. Answered, not answered and marked for review, section by section, as the real interface has it.
  • Full screen, proctored. The test takes over the screen; leaving it three times submits the paper.
  • Answers hidden until you submit. The key, the explanations and your score all arrive together at the end.

About this test

Mensuration Level 2 Practice Quiz on Volume and Surface Area of Solids

This Level 2 mensuration set tests volume and surface area of solids: cubes, cuboids, cylinders, cones, spheres, hemispheres and frustums. It covers recasting one solid into another, water-level rise, percentage change in dimensions and costing problems. Aptitude360 includes a worked solution for every question.

Topics covered in this mensuration area and volume set

  • Melting and recasting spheres, cones and cylinders into other solids
  • Rise in water level when a solid is dropped into a cylinder or tank
  • Volume and curved surface area of a frustum, including bucket capacity
  • Percentage change in volume or surface area when dimensions change
  • Diagonal of a cube and the longest pole that fits in a room
  • Combined solids such as a hemisphere on a cylinder
  • Painting and lining costs for walls and tanks, and hollow pipes
  • Earth dug from a well spread as an embankment

Key mensuration formulas for solids

  • Sphere volume: \( V=\dfrac{4}{3}\pi r^{3} \)
  • Cone volume: \( V=\dfrac{1}{3}\pi r^{2}h \)
  • Cone slant height: \( l=\sqrt{r^{2}+h^{2}} \)
  • Frustum volume: \( \dfrac{1}{3}\pi h(R^{2}+Rr+r^{2}) \)
  • Cylinder curved surface: \( 2\pi rh \)
  • Cuboid diagonal: \( \sqrt{l^{2}+b^{2}+h^{2}} \)

Revision tips for mensuration problems

  • In recasting problems, equate the volumes; the total volume stays the same when a solid is melted.
  • Volume scales with the cube of length and surface area with the square, so a percentage change in radius has a larger effect on volume.
  • Keep pi as a symbol until the last step and substitute the approximation the question specifies only at the end, since terms often cancel neatly.
  • Convert cubic centimetres to litres and metres to centimetres before writing final answers.

Who should practise this Level 2 set

It suits SSC, bank and other aptitude exam aspirants who know the basic formulas of solids and want medium-level application practice.

FAQs about Mensuration (Area & Volume) Practice Questions with Detailed Solutions – Level 2

What is the formula for the volume of a cone?
The volume of a cone is one third of pi times the square of the base radius times the height.
What is the formula for the volume of a frustum?
The volume of a frustum is one third of pi times the height times the sum of the square of the larger radius, the product of the two radii and the square of the smaller radius.
What is the difference between 2D and 3D mensuration?
2D mensuration deals with the perimeter and area of flat shapes such as triangles and circles. 3D mensuration deals with the surface area and volume of solids such as cubes, cylinders, cones and spheres.
How do you solve melting and recasting problems?
Set the volume of the original solid equal to the total volume of the new solids, because melting does not change volume. Then solve for the unknown dimension or the number of pieces.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
Mensuration (Area & Volume) Level 25060 min

Marking & rules

Total marks
50 across 50 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

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