Find the best tutors and institutes for Class 10 Tuition
Q9:
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 12.11. If the height of the cylinder is $10$ cm, and its base is of radius $3.5$ cm, find the total surface area of the article.
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 12.11. If the height of the cylinder is $10$ cm, and its base is of radius $3.5$ cm, find the total surface area of the article.
Solution :
Given:
- Height of the solid cylinder ($h$) = $10$ cm
- Radius of the base of the cylinder ($r$) = $3.5$ cm
- The article is formed by scooping out a hemisphere from each end of the cylinder.
To Find:
The total surface area of the resulting wooden article.
Step 1: Understanding the Surface Area Components
The total surface area of the article consists of three parts:
- The Curved Surface Area (CSA) of the cylinder.
- The Curved Surface Area (CSA) of the top hemisphere.
- The Curved Surface Area (CSA) of the bottom hemisphere.
Formulae to be used:
- CSA of cylinder = $2\pi rh$
- CSA of a hemisphere = $2\pi r^2$
Step 2: Setting up the Equation
Total Surface Area (TSA) = (CSA of cylinder) + (CSA of top hemisphere) + (CSA of bottom hemisphere)
$TSA = 2\pi rh + 2\pi r^2 + 2\pi r^2$
$TSA = 2\pi rh + 4\pi r^2$
$TSA = 2\pi r(h + 2r)$
Step 3: Substituting the Values
Given $r = 3.5$ cm and $h = 10$ cm.
$TSA = 2 \times \frac{22}{7} \times 3.5 \times (10 + 2 \times 3.5)$
[Since $\pi \approx \frac{22}{7}$]
Step 4: Performing the Calculation
First, simplify the radius term: $3.5 = \frac{7}{2}$
$TSA = 2 \times \frac{22}{7} \times \frac{7}{2} \times (10 + 7)$
$TSA = 2 \times \frac{22}{7} \times \frac{7}{2} \times (17)$
Cancel the common factors ($2$ and $7$):
$TSA = 22 \times 17$
$TSA = 374$
Step 5: Final Conclusion
The total surface area is calculated in square centimeters ($cm^2$).
Final Answer: 374 cm²
More Questions from Class 10 Mathematics Surface Areas and Volumes EXERCISE 12.1
- Q1: 2 cubes each of volume $64$ cm$^3$ are joined end to end. Find the surface area of the resulting cuboid.
- Q2: A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is $14$ cm and the total height of the vessel is $13$ cm. Find the inner surface area of the vessel.
- Q3: A toy is in the form of a cone of radius $3.5$ cm mounted on a hemisphere of same radius. The total height of the toy is $15.5$ cm. Find the total surface area of the toy.
- Q4: A cubical block of side $7$ cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
- Q5: A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter $l$ of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
- Q6: A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 12.10). The length of the entire capsule is $14$ mm and the diameter of the capsule is $5$ mm. Find its surface area.
- Q7: A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are $2.1$ m and $4$ m respectively, and the slant height of the top is $2.8$ m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of $₹ 500$ per m$^2$. (Note that the base of the tent will not be covered with canvas.)
- Q8: From a solid cylinder whose height is $2.4$ cm and diameter $1.4$ cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm$^2$.
CBSE Solutions for Class 10 Mathematics Surface Areas and Volumes
Chapters in CBSE - Class 10 Mathematics
Top Tutors who teach Surface Areas and Volumes
Top Tutor
Nigdi, Pune
6 yrs of
Exp
1 hrs of classes completed
400
per hour
Online Classes
Student's Home
I have excellent teaching experience of 7 years with best results with my previous student's from CBSE , STATE and ICSE BOARD'S . Preferably i focus on students personal interest, level of understanding and study methodology. I am here to give best of me to seek best out from my students. I have given seminar on 'Students changing Virtue towards study , Need if time??' . Passionate to guide students towards there destiny
Super Tutor
Badarpur, Delhi
12 yrs of
Exp
154 students
3944 hrs of classes completed
200
per hour
Online Classes
Tutor's home
Akshay is an excellent teacher. He has taught my son in 10 th standard science , with which he understood the concepts clearly and he also gave so many past question papers for my son to work out, all these made my son score 95 in board exams . I would definitely recommend Akshay for students who want to improve and get good scores in science .
Top Tutor
Chopasni Housing Board, Jodhpur
5 yrs of
Exp
Online Classes
Tutor's home
My aim is to prepare students in there best ability and help them achieve good marks. My students scored above 80% in all subjects in class 10th
Top Tutor
Thane West, Thane
20 yrs of
Exp
37 students
5624 hrs of classes completed
350
per hour
Online Classes
This is Prita Chatterjee with 27 years of teaching in the Engineering College and Schools .I teach Maths for all the boards - IB AA(SL& HL) ,IB - AI(HL&SL),Integrated Maths ,MYP ,Cambridge A Level , Additional Maths, IGCSE O Level, ISC, ICSE , CBSE .Presently, I am tutoring students from U.S. France, Austrailia , Netherland , Japan, Singapore, Malaysia , Thailand , Phillipines , Dubai , Riyadh , Doha, and pan India . I would love to teach from basics . .If you would like me to teach your child , kindly let me know ,so we can schedule a demo ,as per suitability.
She is a good teacher with very well and skilled explanations and making sure that students do each and every sum from text book.Hoping that she teaches out of the book&concepts too.:) my only concern is I can’t expect the reply for my messages as quick.
Top Tutor
Sector 19, Noida
3 yrs of
Exp
12 students
613 hrs of classes completed
Online Classes
• 3+ years of teaching experience. • teaching online tuitions of Mathematics for Class 10-12th. • pursued M.Sc. Mathematics from University of Delhi & B.Sc. Mathematical Sciences from University of Delhi. Passionate about solving mathematical problems and I have helped many students to overcome the fear of Maths.
Find more Tutor for Surface Areas and Volumes in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Chennai Mathematics Tutors
- Gurgaon Mathematics Tutors
- Noida Mathematics Tutors
- Hyderabad Mathematics Tutors
- Mumbai Mathematics Tutors
- Ghaziabad Mathematics Tutors
- Chandigarh Mathematics Tutors
- Pune Mathematics Tutors
- Jaipur Mathematics Tutors
- Surat Mathematics Tutors
Download free CBSE - Class 10 Mathematics Surface Areas and Volumes EXERCISE 12.1 worksheets
Download Now
