3 Common Mistakes Committed by Students in Chapter Cylinder, Cone and Sphere

3 Common Mistakes Committed by Students in Chapter Cylinder, Cone and Sphere

Cylinder, Cone and Sphere is a chapter from the unit Mensuration in the ICSE Class 10 syllabus. It involves questions on surface area and volume of solids wherein students commit mistakes in calculations as well as in applying correct formulae.

By Topperlearning Expert 07th Feb, 2024 | 10:22 am

In the ICSE Class 10 syllabus, while attempting questions of the chapter Cylinder, Cone and Sphere from the unit Mensuration insisted on a very clear understanding of a question, understanding the image provided in the question and doing error-free calculations in the given time. This blog explains the areas wherein mistakes are committed by most of the students and also tips to avoid such mistakes.

#1: Doing LENGTHY solutions and WASTING time

As we all are aware, during exams, we need to manage our time to complete the paper on time. And, in some questions, we can save time by doing the calculations smartly. In place of doing lengthy steps, we can save time by making calculations easier.

Consider the below question:

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height of the cylinder is 12 cm and its base is of radius 4.2 cm, find the total surface area of the wooden article. Use .

This question can be solved in two ways as follows:

Solution I

As you can see in the solution I, the individually curved surface area of the cylinder and the surface areas of the two hemispheres are calculated and finally added to get the total surface area of the wooden article.

But in solution II, the two equations are combined by taking common terms and then the total surface area of the wooden article is calculated. By adapting this technique, time is saved as well as chances of calculation errors are reduced.

Solution II

#2: Ignoring the value of Pi (π ) given in the question

Sometimes, in questions, the value of pi that is to be used in the solution is provided.

Use π = 3.14 or Use π = 22/7

But in a hurry, many students ignore the given value of pi and use another one. And, hence, despite doing the solution correctly, the marks are reduced for not taking the right information provided in the question. So, please read the question carefully and take the correct values from the question.

#3 Mistakes committed when DIFFERENT UNITS of measurements are given

Let us understand this error with the help of an example.

Question:

A metal pipe has an inner radius of 10 cm. The pipe is 5 mm thick all around. Find the weight, in kilogram, of 4 metres of the pipe if 1 cm^{3} of the metal weighs 8.5 g.

What do we observe in this question? If you observe, there are different units given in this question such as cm, mm, metres, and gram. And, the final answer is to be calculated in kilograms. Let us understand the areas where students make mistakes in solving this type of question.

Here, the thickness and length of the pipe need to be converted into cm. Why cm? Because the weight of the metal is given for 1 cm^{3} capacity of pipe.

Conversion of Thickness of the pipe and length of the pipe in cm

The thickness of the pipe is given in mm which has to be converted into cm. But many a time, students write thickness as 5 mm only.

Writing the final answer in kg

Once the volume of the pipe is found in cubic cm or cm^{3}, its weight has to be found in kilogram. But, in question, it is stated that 1 cm^{3} of metal weighs 8.5 g. In this case, we find the weight of the pipe in grams by multiplying the volume by 8.5 grams and then converting the grams into kilogram by dividing by 1000.

Most of the time, students fail to convert the gram into kilogram resulting in loss of marks.

PRACTICE QUESTIONS

Question 1: Find the radius of the base of the cylinder whose volume and height are 1.54 cm^{3} and 1 m respectively.

Hint: Convert height into cm. For the detailed solution click here.

Question 2: A metallic sphere of diameter 1 cm is to be melted and recast into a hollow sphere of thickness 1 mm. Find the internal and external radii of the sphere.

Hint: Find the volume of hollow sphere and equate it with the volume of solid sphere to get internal and external radius. For the detailed solution, click here.

CONCLUSION

Students, if you take care of all the above-mentioned mistakes, no doubt you can score good marks in your exams. Avoid lengthy steps and do the calculations carefully. A huge amount of quality resources is available at TopperLearning for your understanding such as Revision Note providing complete explanations of the chapter, Assertion and Reasoning Questions for practice.

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