What is a Parallelogram Parallelogram definition states that a parallelogram is a four-sided figure which has two pairs of parallel sides. Some of theproperties of parallelograms are as follows: The opposite sides of a parallelogram are of the same length. The opposite angles of a parallelogram are congruent. The overall angles of parallelogram adds up to 360 degree. These are some of the parallelogram proeprties.The area of a parallelogram is also the same as the degree of thevector cross product of two adjacent sides. The area of a parallelogram can be calculated by using the formula shown below, Parallelogram Know More About Scatter Plot Worksheet
Area = b Ă— h Sq. Units Perimeter = 2(b + h) Units. Where, b is the base of the parallelograms and h is the height of the parallelograms. The area of a parallelograms is two times the area of a triangle created by one of its diagonals The area of a parallelogram is equal to the size of the vector cross product of two adjacent sides. Perimeter of a Parallelogram The perimeter of a parallelogram can be measured in a two dimensional figure. It is the outer layer or the border of the area of the two dimensional shape. It is also known as circumference. For example, if a garden is covered with a fence then the perimeter of the fence covered garden will be the length of the fence. Here we are going to see the perimeter of the parallelogram. Learn More Simple Division Worksheets
The perimeter of a parallelogram = 2 ( side1 + side2 ) Solving Problems on Parallelograms Below are some solved problems on parallelograms Example 1: Find the area of the parallelogram, given length = 5 cm and base = 6 cm Solution : Area of parallelogram = b x h =5x6 Area of parallelogram = 30 cm2 Example 2: Find the area and perimeter of the parallelogram, whose length = 15 cm and base = 3 cm. Solution: Area of parallelogram = b x h = 15 x 3 Area of parallelogram = 45 cm2 Perimeter of parallelogram = 2(b + h) = 2(15 + 3)
Formula For Volume Of A Sphere Volume of a Sphere is a measurement of the occupied units of a Sphere. The volume of a Sphere is represented by cubic units like cubic centimeter, cubic millimeter and so on. Volume of a Sphere is the number of units used to fill a Sphere. Generally the volume of a solid is calculated as the area of the base times its height as long the area is constant throughout the height of the solid. But this concept can not be directly applied to find the volume of a sphere because the area changes with every cross section of the sphere. Volume of a Sphere Formula Formula for Volume of a Sphere was found by Archimedes. Archimedes found after several experiments that the volume of a sphere and also its surface area is exactly rd of the volume and the surface area of a cylinder with the same outer dimensions.
In the above diagram, let r be the radius of the sphere. Since the over all dimensions of both the sphere and the cylinder are the same, the height of the cylinder is 2r. Under this condition, Volume of a cylinder = Area of the base x Height of the cylinder. = πr2 x 2r = 2πr3 Therefore, as per Archimedes formula the volume of the sphere is, ( )( 2πr3) = ( )πr3 So much happy about this result by himself, Archimedes wished a cylinder and globe be placed on his tomb! (This wish was fulfilled) Volume of a Sphere Examples Given below are some examples to find the volume of a sphere Example 1: Read More About Free Online Tutoring For Math
The sphere has a radius of 8.2 cm. Solve for volume of sphere. Solution: Given: Radius (r) = 8.2 cm Formula: Volume of the sphere (v) = 43 π r3 cubic unit = 43 x π x (8.2)3 =43 x 3.14 x 551.368 Volume of the sphere (v) = 2308.39 cm3 Example 2: The sphere has radius of 8.3 m. Solve for volume of sphere. Solution: Given: Radius (r) = 8.3 m
Formula: Volume of the sphere (v) = 43 π r3 cubic unit = 43 x π x (8.3)3 =43 x 3.14 x 571.78 Volume of the sphere (v) = 2393.88 m3 Volume of a Sphere Practice Problems 1. The sphere has radius of 5.8m. Find the volume of sphere. Answer: Volume (V) = 817.28 m3 2. The sphere has radius of 6.9 cm. Find the surface area and volume of sphere. Answer: Volume (V) = 1376.05 cm3