12 Questions
What is the formula for calculating the perimeter of a rectangle?
P = 2l + 2w
Which formula is used to find the surface area of a sphere?
SA = 4πr²
What is the surface area formula for a 3D prism?
SA = 2l² + 2lw
How is the area of a parallelogram calculated?
A = bh
What is true about 3D shapes?
They have length, width, and height
Which formula is used to calculate the volume of a cube?
$V = l^3$
What is mensuration?
The branch of mathematics concerned with measuring quantities such as length, area, volume, and angle
How is the volume of a rectangular box calculated?
$V = l \times w \times h$
What is the formula for the volume of a sphere?
$V = (4/3)\pi r^3$
How is the area of a rectangle calculated?
$A = lw$
What does the area of a triangle depend on?
Height and base
How is the surface area of a cube calculated?
$A = 6s^2$
Study Notes
Mensuration
Mensuration is the branch of mathematics concerned with measuring quantities such as length, area, volume, and angle. It involves using formulas to calculate these measurements from given data. In this article, we will discuss various aspects of mensuration, including volume, area, perimeter, 3D shapes, and surface area.
Volume
Volume is a measure of the amount of space occupied by a three-dimensional object. The volume of a rectangular box, for example, can be calculated using the formula:
V = l × w × h
where V is the volume, l is the length, w is the width, and h is the height of the box.
Solid Figures
Solid figures are three-dimensional objects that have length, width, and height. Some examples of solid figures include cubes, spheres, and cylinders. The volume of these figures can also be calculated using specific formulas:
- Cube: V = s³, where s is the length of one side.
- Sphere: V = (4/3)πr³, where r is the radius.
- Cylinder: V = πr²h, where r is the radius and h is the height.
Area
Area is a measure of the amount of space occupied by a two-dimensional object. The area of a rectangle, for instance, can be calculated using the formula:
A = l × w
where A is the area, l is the length, and w is the width.
Polygons
Polygons are two-dimensional shapes with three or more sides. The area of a polygon can be calculated using the following formulas:
- Triangle: A = (1/2)bh, where b is the base and h is the height.
- Rectangle: A = l × w.
- Parallelogram: A = bh, where b is the base and h is the height.
Perimeter
Perimeter is the total distance around an object. For example, the perimeter of a rectangle can be calculated using the formula:
P = 2l + 2w
where P is the perimeter, l is the length, and w is the width.
3D Shapes
3D shapes are three-dimensional figures that have length, width, and height. Some examples of 3D shapes include cubes, spheres, and cylinders. These shapes can be used to solve various problems in mensuration, such as finding the volume, surface area, or perimeter of a given shape.
Surface Area
Surface area is the total area of a two-dimensional object. The surface area of a sphere, for example, can be calculated using the formula:
SA = 4πr²
where SA is the surface area and r is the radius of the sphere.
3D Prism
The surface area of a 3D prism can be calculated using the formula:
SA = 2l² + 2lw
where SA is the surface area, l is the length, and w is the width.
In conclusion, mensuration is a vital aspect of mathematics that involves measuring various quantities such as volume, area, perimeter, and surface area. By understanding and applying the formulas and concepts discussed in this article, one can effectively solve a wide range of problems related to mensuration.
Test your knowledge of mensuration formulas for calculating volume, area, perimeter, and surface area in 2D and 3D shapes. This quiz covers topics such as calculations for cubes, spheres, cylinders, rectangles, triangles, and more.
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