Ncert Maths Class 8 Try These Solutions Mensuration

Ever sat staring at a math textbook, reached a page titled "Try These," and felt a sudden urge to close the book entirely? You aren't alone. Practically speaking, those little boxes scattered throughout the NCERT Class 8 math chapters aren't just extra homework. They are actually the "stress tests" of the curriculum.

If you can breeze through them, you've mastered the concept. Day to day, if you hit a wall, it means there's a gap in your understanding that will eventually bite you in higher grades. Mensuration is one of those chapters where that gap becomes a canyon. It's the jump from simple counting to calculating the space inside and around objects, and it's where most students start feeling like math is just a series of confusing formulas.

What Is Mensuration in Class 8

In plain English, mensuration is the study of measurement. We aren't talking about measuring your height with a tape measure—though that is technically part of it. We are talking about the math used to quantify the size of shapes.

Area and Perimeter

At this stage, you are moving beyond just finding the length of a line. You are looking at the boundary of a shape (perimeter) and the flat surface it covers (area). Think of it like this: if you were building a fence around a garden, you'd need the perimeter. If you were buying grass to cover that garden, you'd need the area.

Surface Area and Volume

This is where things get three-dimensional. Instead of just flat shapes like squares or rectangles, you start dealing with solids like cubes, cuboids, and cylinders. Now, you aren't just looking at the "flat" part. You're looking at the total area of all the faces combined (surface area) and the actual amount of space inside the object (volume). It's the difference between looking at a drawing of a box and actually filling that box with sand.

Why It Matters

Why do we spend so much time on this? Because the world isn't flat. Everything you interact with—from the screen you are reading this on to the room you are sitting in—has volume and surface area.

If you don't grasp these concepts now, you'll struggle when you hit Class 9 and 10, where the geometry gets much more complex. But even more practically, mensuration is used in construction, packaging, interior design, and even cooking. Even so, if a chef needs to know how much liquid a pot can hold, they are using volume. If a painter needs to know how much paint to buy for a room, they are using surface area. Understanding this now builds the "spatial reasoning" your brain needs for almost every STEM career.

How to Solve Mensuration Problems

Solving these problems isn't about memorizing a list of formulas. And it's about understanding the relationship between dimensions. When you see a "Try These" problem, don't jump straight to the math. Follow a process.

Step 1: Visualize the Shape

Before you touch a calculator, draw it. Even a messy sketch helps. If the problem describes a cylinder, draw a tube. If it's a cuboid, draw a box. This helps you identify which "faces" you need to account for.

Step 2: List Your Knowns and Unknowns

Write down everything the problem tells you.

• Length (l) =?
• Width (w) =?
• Height (h) =?
• Radius (r) =?

Once you see what you have, you'll realize what's missing. Most "Try These" questions are designed to give you three pieces of information and ask for a fourth.

Step 3: Choose the Right Formula

This is where most people trip up. They see "area" and use a "volume" formula.

• For a Cuboid:
  • Area of one face = $l \times w$
  • Total Surface Area = $2(lw + wh + lh)$
  • Volume = $l \times w \times h$
• For a Cylinder:
  • Curved Surface Area = $2\pi rh$
  • Total Surface Area = $2\pi r(r + h)$
  • Volume = $\pi r^2h$

Step 4: The Unit Check

This is the silent killer of math grades. If the length is in centimeters and the width is in meters, your answer will be nonsense. Always convert everything to the same unit before you start calculating. And remember, area is always in square units (cm², m²) and volume is always in cubic units (cm³, m³).

For more on this topic, read our article on how does a generator make electricity or check out what does it mean for points to be collinear.

Common Mistakes / What Most People Get Wrong

I've seen students struggle with the same three things over and over again. If you want to master NCERT Class 8 mensuration, avoid these traps.

Confusing Surface Area with Volume

This is the big one. Students often see a question about "how much water a tank can hold" and try to calculate the surface area instead. Remember: Volume is capacity (inside). Surface area is the skin (outside).

Forgetting the "2" in Formulas

In the formula for the surface area of a cuboid, $2(lw + wh + lh)$, that "2" is there because a box has a top and a bottom, a front and a back, and two sides. If you forget that 2, you're only measuring half the box.

Miscalculating $\pi$ (Pi)

NCERT often tells you to use $22/7$ or $3.14$. If you switch between them mid-problem, your answer will be slightly off. Stick to the instruction given in the specific problem to keep your calculations consistent.

Practical Tips / What Actually Works

If you are working through the "Try These" sections and getting stuck, here is how to actually fix it.

• Work Backwards: If a problem gives you the volume and asks for the height, don't panic. Set up the formula, plug in what you know, and use basic algebra to isolate the missing variable.
• Use Real Objects: If you're struggling with the concept of a cylinder, grab a soda can. Look at the circular top and the curved side. It makes the math feel much less abstract.
• Check Your Logic: After you get an answer, ask yourself: "Does this make sense?" If you calculate the volume of a small matchbox and get 500 cubic meters, you know something went wrong with your decimal points.
• Don't Skip the "Try These" Boxes: I know they look like extra work, but they are actually there to catch your mistakes while they are still small. It's much better to realize you don't understand surface area in Class 8 than to realize it in Class 11.

FAQ

Why is the area of a circle $\pi r^2$?

It's hard to visualize, but imagine cutting a circle into many tiny slices and rearranging them into a shape that looks like a rectangle. The length of that "rectangle" is half the circumference ($\pi r$), and the width is the radius ($r$). Multiply them, and you get $\pi r^2$.

What is the difference between Lateral Surface Area and Total Surface Area?

Lateral Surface Area only counts the "sides" (the curved part of a cylinder or the vertical faces of a box). Total Surface Area counts the sides plus* the top and the bottom.

How do I handle units in mensuration?

Always ensure all measurements are in the same unit before you start multiplying. If you have one measurement in cm and another in m, convert them both to cm first. It's much easier than trying to convert the final answer.

Is there a difference between 2D and 3D mensuration?

Yes. 2D mensuration deals with flat shapes (area and perimeter) like squares and triangles. 3D mensuration deals with solid objects (volume and surface area) like cubes and cylinders.

Mastering these concepts isn't about being a "math person.That's why " It's about being a careful person. It's about looking at a shape, identifying its parts, and applying the right logic.

...physical objects they represent, the memorization takes care of itself.

The formulas for the volume of a cylinder or the surface area of a sphere weren't invented to torture students; they were derived to describe how much space an object occupies or how much material is needed to build it. When you look at a water tank and instinctively break it down into a circular base and a height, or see a cardboard box and mentally flatten it into a net of six rectangles, you have stopped "doing mensuration" and started thinking spatially*.

That shift—from rote application to structural understanding—is the real goal of this chapter. The exams will ask for answers in cubic centimeters or square meters, but the skill you are actually building is the ability to deconstruct complex 3D problems into manageable 2D steps. Keep your units consistent, draw your diagrams, and trust the logic. The numbers will follow.