Suppose a person has a cuboid and you want to paint this cuboid from the outer, and you want to know how much is required to paint this cuboid. For this, the total area of the outer layer should be calculated, and this area is called the surface area of any object. Therefore, surface area is the total outer space of any three-dimensional object. After painting this cuboid, if a person wants to fill this cuboid with water, then how much water is needed to fill this cuboid? To determine the answer to this question person should know the amount of space within this cuboid, and this amount of space is called the volume of the cuboid. Therefore, the amount of space within any three-dimensional object is called the volume.
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In the NCERT Books exercise 12.1, Class 10 Maths, we have to find the surface area of the combined solids. Some of these solids are cylinders with both sides hemispheres, and cones with a hemisphere on top. Surface area can be categorised into two types of surface areas: the curved surface area and the total surface area. 10th class Maths exercise 12.1 answers are designed as per the students' demand, covering comprehensive, step-by-step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in-depth understanding of concepts. These NCERT solutions Class 10 Maths ex 12.1 present us with the surface area of a combination of Solids. Some solids, such as the cuboid, cone, cylinder, and sphere, are recognisable to you from Class IX. You've also learned how to calculate their volumes and surface areas. In our daily lives, we come across a variety of solids that are made up of two or more of the fundamental solids.
Q1. 2 cubes, each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Answer:
We are given that volume of the cube
Also, the volume of a cube is given by
Thus:
Now, according to the question, we have combined the two cubes so that the edge lengths of the formed cuboid are 4 cm, 4 cm, and 8 cm.
The surface area of a cuboid is :
or
or
or
Thus, the area of the formed cuboid is 160 cm².
Answer:
Since the vessel consists of a hemisphere and a cylinder, its area is given by :
Area of vessel = Inner area of the cylinder(curved) + Inner area of the hemisphere
The inner surface area of the hemisphere is :
or
or
And the surface area of the cylinder is :
or
or
Thus, the inner surface area of the vessel is
Answer:
The required surface area of the toy is given by :
Area of toy = Surface area of hemisphere + Surface area of the cone
Firstly, consider the hemisphere:
The surface area of a hemisphere is
or
or
Now, for the cone we have:
The surface area of a cone
Thus, we need to calculate the slant of the cone.
We know that:
or
or
or
Thus surface area of a cone
or
or
Hence, the total surface area of toy =
Answer:
It is given that the hemisphere is mounted on the cuboid, thus, the hemisphere can take on complete as its diameter (which is maximum).
Thus, the greatest diameter of the hemisphere is 7 cm.
Now, the total surface area of the solid = Surface area of the cube + Surface area of the hemisphere - Area of the base of the hemisphere (as this is counted on one side of the cube)
The surface area of the cube is :
Now the area of a hemisphere is
And the area of the base of a hemisphere is
Hence, the surface area of the solid is
Answer:
It is given that the diameter of the hemisphere is equal to the edge length of the cube.
The total surface area of the solid is given by :
The surface area of a solid = Surface area of the cube + Surface area of the hemisphere - Area of the base of the hemisphere
The surface area of the cube
And the surface area of the hemisphere:
Area of the base of the hemisphere:
Thus, the area of the solid is:
Answer:
It is clear from the figure that the capsule has a hemisphere and cylinder structure.
The surface area of the capsule = 2 (Area of the hemisphere) + Area of the cylindrical part
Area of hemisphere
or
or
And the area of the cylinder
or
or
Thus, the area of the solid is :
Answer:
The canvas will cover the cylindrical part as well as the conical part.
So, the area of canvas = Area of cylindrical part (curved) + Area of the conical part
Now, the area of the cylindrical part is
or
or
And the area of the cone is
or
or
Thus, the area of the canvas
or
Further, it is given that the rate of canvas per m 2 is = Rs. 500.
Thus, the required money is
Answer:
Firstly, we need to calculate the slant height of the cone :
or
or
or
Now, the total surface area of the solid can be calculated as :
The surface area of a solid = Surface area of cylinder + Surface area of cone + Area of base of the cylinder
The surface area of the cylinder is
or
or
Now, the surface area of a cone
or
or
And the area of the base of the cylinder is
or
or
Thus required area of the solid = 10. 56 + 5.50 + 1.54 = 17.60 cm2 .
Thus total surface area of the remaining solid to the nearest cm2 is 18 cm2.
Answer:
The required surface area is given by :
The surface area of the article = Surface area of the cylindrical part + 2 (Surface area of the hemisphere)
Now, the area of the cylinder
or
or
And the surface area of the hemisphere:
or
or
Thus, the required area
Also Read
Also See:
Students must check the NCERT solutions for class 10 of the Mathematics and Science Subjects.
Students must check the NCERT Exemplar solutions for class 10 of the Mathematics and Science Subjects.
Frequently Asked Questions (FAQs)
The most commonly used value of pi used in exercise 12.1 Class 10 Maths is
There are many basic question in which we have to find the total surface of combination of solid or real life objects such as tents , capsules toys etc but some are direct that only ask about the solid
The total number of examples that have been solved before the class 10 Maths chapter 12 exercise 12.1 is four
The total number of questions in the NCERT solutions for Class 10 Maths chapter 12 exercise is nine.
Curved surface area of hemisphere used is =2πr²
Curved surface area of hemisphere used in 2πrl
We can use surface area in many places in our daily life, for example identifying the amount of paint require to paint object , determining the cost of things like clothes , covers and canvas tents
On Question asked by student community
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The CM Shri School Admission Test was conducted for students seeking quality education.
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