i just want to know the correct method to find out the volume and surface area of prism and cylinder. also the formula of perimeter of semi circle and complete circle also its area and how to find out the shaded part of area. with methods please post some examples for clear understanding.
google will provide numerous illustrations, formulas and discussions. Just search for those key words and you will find everything you want.
Sure! I can help you with that. Let's start with the volume and surface area of a prism and a cylinder.
Volume of a Prism:
To find the volume of a prism, you need to multiply the area of the base by the height of the prism. The formula is:
Volume = Base Area × Height
Surface Area of a Prism:
To find the surface area of a prism, you need to calculate the sum of the areas of all its faces. The formula varies depending on the shape of the base.
For a Rectangular Prism:
Surface Area = 2 × (length × width + length × height + width × height)
For a Triangular Prism:
Surface Area = Base Area + Perimeter of the Base × Height + 2 × (Area of Each Triangular Face)
For a Cylinder:
Volume of a Cylinder:
To find the volume of a cylinder, you need to multiply the area of the base (which is the area of a circle) by the height of the cylinder. The formula is:
Volume = π × r^2 × height
Surface Area of a Cylinder:
To find the surface area of a cylinder, you need to calculate the sum of the areas of the two bases and the lateral surface area. The formula is:
Surface Area = 2 × π × r^2 + 2 × π × r × height
Moving on to the perimeter and area of a semicircle and a complete circle:
Perimeter of a Semicircle:
The perimeter of a semicircle is the sum of the length of the straight edge (diameter) and half the circumference of the circle. The formula is:
Perimeter = π × r + 2r
Area of a Semicircle:
The area of a semicircle is half the area of a full circle. The formula is:
Area = 0.5 × π × r^2
Perimeter of a Circle:
The perimeter of a circle is also known as the circumference. The formula is:
Perimeter = 2 × π × r
Area of a Circle:
The area of a circle is given by the formula:
Area = π × r^2
To find the shaded part of an area, you need to subtract the area of the shaded portion from the area of the whole shape. This can be done by finding the area of the whole shape and subtracting the area of the shaded portion.
Here are some examples for better understanding:
1. Example for Volume and Surface Area of a Rectangular Prism:
Given: Length = 5 cm, Width = 3 cm, Height = 7 cm
Volume = Base Area × Height
Volume = (5 cm × 3 cm) × 7 cm
Volume = 105 cm^3
Surface Area = 2 × (length × width + length × height + width × height)
Surface Area = 2 × (5 cm × 3 cm + 5 cm × 7 cm + 3 cm × 7 cm)
Surface Area = 166 cm^2
2. Example for Volume and Surface Area of a Cylinder:
Given: Radius = 4 cm, Height = 8 cm
Volume = π × r^2 × height
Volume = π × (4 cm)^2 × 8 cm
Volume = 321.87 cm^3 (approx.)
Surface Area = 2 × π × r^2 + 2 × π × r × height
Surface Area = 2 × π × (4 cm)^2 + 2 × π × 4 cm × 8 cm
Surface Area = 301.59 cm^2 (approx.)
I hope these explanations and examples help you understand how to calculate the volume, surface area, perimeter, and area of various shapes. Let me know if you have any more questions!