Mensuration Formula – 2D and 3D shapes
Mensuration Formula (2D and 3D shapes)
Definition:
Mensuration is the part of mathematics that deals with the length, area, and volume of different geometrical figures.
Type of shapes and differences:
The two things that are broadly dealt with in Mensuration are two-dimensional figures and three-dimensional solids. The detailed description, along with their differences, is attached below:
Important terms:
2D mensuration formula:
Mensuration formula 3D:
Solved Examples:
1. Calculate the area of a square with side 5 cm.
The area of a square of side 5cm is A=L^{2}=5^{2}=25 \mathrm{~cm}^{2}
2. Calculate the perimeter of a rectangle having a length of 10 cm and breadth of 5 cm.
The perimeter of a rectangle with length 10 cm and breadth 5 cm is 2( l + b) = 2(10 + 5) = 30 cm.
3. What is the area of a right-angled triangle with two of its perpendicular sides as 3 and 4 cm?
The area of a right angled triangle with two of its perpendicular sides as 3 cm and 4 cm is:
A = ½ x b x h = 0.5 x 3 x 4 = 6 \mathrm{~cm}^{2}.
4. Calculate the volume of a cone having a radius of 7 cm and height of 5 cm?
The volume of a cone with a radius of 7 cm and height of 5 cm is:
(1 / 3) \pi r^{2} h=256.67 \mathrm{~cm}^{3}
5. What is the total surface area and curved surface area of a cylinder with a radius of 14 cm and height of 10 cm?
The total surface area of a cylinder with radius 14 cm and height 10 cm is:
2 \pi r h+2 \pi r^{2}=2112 \mathrm{~cm}^{2}
The curved surface area of a cylinder with radius 14cm and height 10cm is:
2 \pi r h=880 \mathrm{~cm}^{2}
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Frequently Asked Questions
Q1. What is the area of a square with side ‘a’ cm?
Ans: The area of a square with side ‘a’ cm is a^{2}.
Q2. What is the area of a circle with radius ‘r’ cm?
Ans: The area of a circle with radius ‘r’ cm is \pi r^{2} .
Q3. What is the formula for calculating volume of a cube with side ‘a’?
Ans: The volume of a cube is equal to {\text {a}}^3 where ‘a’ is the length of each side of the cube.
Q4. What is the formula for calculating the volume of a sphere having a radius ‘r’?
Ans: The volume of a sphere with radius ‘r’ is (4/3) \pi r^{3}.