Exercise 9.4 class 8 solution-Introduction
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Exercise 9.4 class 8 solution- what are solid shapes ?
Solid shapes, also known as three-dimensional (3D) shapes or solids, are geometric objects that exist in three-dimensional space and have volume in addition to having length and width. These shapes are not flat; they have depth. Solid shapes are encountered in various aspects of geometry, mathematics, and real-world applications. Here are some common examples of solid shapes:
Cube: A cube is a six-sided, regular polyhedron with all sides (faces) being congruent squares. It has 12 edges and 8 vertices. The cube has a total of six equal square faces.
Rectangular Prism (or Rectangular Box): This is a rectangular solid with six faces, 12 edges, and 8 vertices. It has three pairs of congruent, rectangular faces.
Sphere: A sphere is a perfectly round, 3D object with no corners, edges, or flat faces. It is defined by its center and a constant radius.
Cylinder: A cylinder has two circular bases and a curved surface connecting the bases. It can be right or oblique (slanted). The volume of a cylinder is calculated using the formula πr²h, where ‘r’ is the radius of the base and ‘h’ is the height.
Cone: A cone has a circular base and a single curved surface extending from the base to a single vertex (apex). The volume of a cone is calculated using the formula (1/3)πr²h.
These are just a few examples of solid shapes. Solid geometry deals with the study of these three-dimensional objects, their properties, volumes, surface areas, and various applications.
Exercise 9.4 class 8 solution-surface area of cuboid ,cube and cylinder.
Here are the formulas for calculating the surface area of a cuboid, a cube, and a cylinder:
- Surface Area of a Cuboid:A cuboid has six faces, and to find its total surface area, you need to calculate the area of each face and then add them up. The formula for the surface area of a cuboid is:Surface Area = 2lw + 2lh + 2wh
- ‘l’ is the length of the cuboid.
- ‘w’ is the width of the cuboid.
- ‘h’ is the height of the cuboid.
- Surface Area of a Cube:
- A cube is a special case of a cuboid where all sides (faces) are congruent squares. To find the surface area of a cube, you can use the formula:
- Surface Area = 6s²
- ‘s’ is the length of one side of the cube (all sides are equal in a cube).
- Surface Area of a Cylinder:A cylinder has two circular bases and a curved lateral surface. The formula for the surface area of a cylinder is the sum of the areas of the two circular bases and the lateral surface area:Surface Area = 2πr² + 2πrh
- ‘r’ is the radius of the circular base.
- ‘h’ is the height of the cylinder.
- So, to find the surface area of a cuboid, cube, or cylinder, you’ll need to know the relevant dimensions (length, width, height, radius) and use the appropriate formula for each shape.
Example 9.4.1. Find the total surface area and lateral surface area of cube having side 10cm.
Example 9.4.2 what will happen to the surface area of the cube if its edge is doubled ?
Example 9.4.3 Three cubes each of side 4cm are joined end to end .find the surface area of the cuboid so formed .
solve.Calculate the length, width, and height of the cuboid based on the cubes’ arrangement:
- The length of the cuboid will be equal to the combined lengths of the three cubes. Each cube has a side length of 4 cm, so the length of the cuboid is 4 cm × 3 = 12 cm.
- The width of the cuboid will be equal to the side length of one cube, which is 4 cm.
- The height of the cuboid will also be equal to the side length of one cube, which is 4 cm.
Now that you have the dimensions of the cuboid (length, width, and height), you can find its surface area using the formula for the surface area of a cuboid:
Exercise 9.4 class 8 solution- Surface area of right circular cylinder.
The surface area of a right circular cylinder can be calculated using the following formula:
Surface Area = 2πr² + 2πrh
- ‘r’ is the radius of the circular base of the cylinder.
- ‘h’ is the height of the cylinder.
The formula accounts for the two circular bases and the curved lateral surface of the cylinder. To find the surface area, simply plug in the values for the radius and height of the cylinder into the formula, and then perform the calculations.
Exercise 9.4 class 8 solution- exercise preview
Our Exercise 9.4 Preview is designed to give you a taste of what’s in store. You’ll find a selection of math problems and questions that challenge your analytical and problem-solving skills. It’s a glimpse into the wonderful world of math exercises that will not only sharpen your mathematical prowess but also help you build the confidence you need to excel in your Class 8 studies.
Exercise 9.4 class 8 solution- solution pdf
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So, get ready to unlock the world of mathematics and explore Exercise 9.4 class 8 solutions that will help you not only in your exams but also in building a strong foundation for future mathematical adventures. Click, download, and excel in math! Your math journey is about to get a whole lot easier.9.4