CBSE Class 10th Surface Area of a Combination of Solids Details & Preparations Downloads
Geometry, the branch of mathematics that deals with the properties and relationships of points, lines, angles, surfaces, and solids, has been a fascinating subject for centuries. Among the many concepts it encompasses, the surface area of a combination of solids stands out as a captivating and intricate topic. In this blog post, we will embark on a journey to understand the nuances of calculating the surface area when different solids are combined.
Unlocking Geometric Excellence: CBSE NCERT Download on Calculating the Surface Area of Combined Solids
The surface area of an object is given by the total area of the surface that an object occupies, or we can say the total area of all the surfaces of any threedimensional figure. The surface area of figures other than cubes or cuboids can be calculated as the lateral area of the figure plus its every base, in case if prism and cylinder are the same then we can take it as twice the area of the base. The surface area of any given figure can be calculated with the help of the example of a gift as a threedimensional figure and let the surface area be the wrapping paper, so the amount of wrapping paper used to cover the gift is the surface area of the given threedimensional figure. Surface area can be given by the following formula:
Surface area = Lateral area + (n * base)
where, n = no. of bases present (n = 2 for prism/ cylinder, n = 1 for pyramids/ cones, and n = 0 for spheres/ circles)
Surface area can be further divided into 2 types such as:

Total surface area – The area including the base and the curved part is called a total surface area.

Curved surface area – The area of the curved part excluding the base is called the curved surface area.
Volumes of any given object can be said as the amount of liquid it can contain in it. Basically, the quantity enclosed by the given threedimensional objects is called the volume of that object. The volume of the one dimensional (e.g., lines), as well as the twodimensional object (e.g., squares), are considered zero as the volume is considered as quantity. The basic properties to find the volume of any given object are as follows:

Any given object has the volume of length * breadth * height (V = lwh).

The total volume of any given object is the sum of all nonoverlapping regions.

Exactly the same when superimposing figures have the same volume.

Depending on the unit cube, every polyhedral region has a unique volume.
Volume can be calculated with the help of the following formulas for different figures:
Volume of the sphere (V) = (4/3) π x (radius)^{3}
Volume of prism or cylinder (V) = base area x height
Volume of pyramid or cone (V) =
(13)(13)
x base area x height
I. Understanding Basic Surface Area Concepts:
Before delving into the complexities of combining solids, it's crucial to have a solid grasp of the basics. The surface area of a single solid, such as a cube, cylinder, or sphere, can be calculated using specific formulas. Briefly revisiting these formulas will serve as a foundation for our exploration.
II. The Challenge of Combining Solids:
When two or more solids are combined, determining the total surface area becomes a more intricate task. Consider scenarios where a cube is placed on top of a cylinder, or a cone is attached to a rectangular prism. In such cases, each individual solid's surface area must be calculated, and then the overlapping or shared areas need to be considered.
III. Methodology for Combined Surface Area:

Calculate Individual Surface Areas: Begin by computing the surface area of each solid using the appropriate formulas.

Consider Shared Faces: Identify the faces or surfaces that are shared between the combined solids. These shared areas must be included only once in the total surface area.

Summation of Surface Areas: Add up the individual surface areas and the shared areas to obtain the total surface area of the combination of solids.
IV. Realworld Applications:
Understanding the surface area of a combination of solids is not just a theoretical exercise. This concept finds practical applications in various fields, such as architecture, engineering, and manufacturing. Architects use these calculations to optimize material usage, while engineers apply them to design efficient structures and machinery.
CBSE Class 10th Downloadable Resources:
1. CBSE Class 10th Topic Wise Summary  View Page / Download 
2. CBSE Class 10th NCERT Books  View Page / Download 
3. CBSE Class 10th NCERT Solutions  View Page / Download 
4. CBSE Class 10th Exemplar  View Page / Download 
5. CBSE Class 10th Previous Year Papers  View Page / Download 
6. CBSE Class 10th Sample Papers  View Page / Download 
7. CBSE Class 10th Question Bank  View Page / Download 
8. CBSE Class 10th Topic Wise Revision Notes  View Page / Download 
9. CBSE Class 10th Last Minutes Preparation Resources (LMP)  View Page / Download 
10. CBSE Class 10th Best Reference Books  View Page / Download 
11. CBSE Class 10th Formula Booklet  View Page / Download 
Being in CBSE class 10th and considering the board examinations you must be needing resources to excel in your examinations. At TestprepKart we take great pride in providing CBSE class 10th all study resources in downloadable form for you to keep you going.
Below is the list of all CBSE class 10th Downloads available on TestprepKart for both Indian and NRI students preparing for CBSE class 10th in UAE, Oman, Qatar, Kuwait & Bahrain.
SAMPLE PRACTICE QUESTION
Q1: What does the term "combination of solids" refer to in the context of surface area?
Ans: A combination of solids involves two or more threedimensional shapes (solids) joined or intersecting to form a composite object.
Q2: How is the surface area calculated for a combination of solids?
Ans: The surface area of a combination of solids is found by summing up the individual surface areas of each solid within the combination.
Q3: Can you provide an example of a combination of solids and how to calculate its surface area?
Ans: Certainly! Consider a rectangular prism with a cylindrical hole drilled through it. To find the surface area, calculate the sum of the surface areas of the rectangular prism and the cylindrical hole.
Q4: What is the significance of identifying and calculating the surface area of combined solids?
Ans: Identifying and calculating the surface area of combined solids is crucial in various applications, such as designing objects with complex shapes, optimizing material usage, and understanding the overall geometric characteristics.
Q5: How does the surface area of combined solids relate to the individual surface areas of each solid?
Ans: The surface area of combined solids is the sum of the individual surface areas of each solid within the combination. It accounts for the external surfaces of the entire composite object.