Important Formulas: Surface Area & Volumes

# Important Formulas: Surface Area & Volumes | Mathematics for EmSAT Achieve PDF Download

## Important Points

1. Mensuration
It is branch of mathematics which is concerned about the measurement of length ,area and Volume of plane and Solid figure
2. Perimeter
(a)  The perimeter of plane figure is defined as the length of the boundary
(b) It units is same as that of length i.e. m ,cm,km
3. Area
(a) The area of the plane figure is the surface enclosed by its boundary
(b) It unit is square of length unit. i.e. m2 , km2
4. Volume
Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid. Its units are always ''cubic", that is, the number of little element cubes that fit inside the figure.

Volume Unit conversion

Surface Area and Volume of Cube and Cuboid

Surface Area and Volume of Right circular cylinder

Surface Area and Volume of Right circular cone

Surface Area and Volume of sphere and hemisphere

Sphere

Hemisphere

Type and Measurement

• Surface area of Sphere - 4πr2
• Volume of Sphere- 4/3πr3
• Curved Surface area of hemisphere 2πr2
• Total Surface area of hemisphere - 3πr2
• Volume of hemisphere - 2/3πr3
• Volume of the spherical shell whose outer and inner radii and 'R' and V respectively - 4/3π(R3 - r3)

How the Surface Area and Volume are determined

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## FAQs on Important Formulas: Surface Area & Volumes - Mathematics for EmSAT Achieve

 1. What is the formula for finding the surface area of a rectangular prism?
Ans. The formula for finding the surface area of a rectangular prism is given by 2(lw + lh + wh), where l is the length, w is the width, and h is the height of the prism.
 2. How do you calculate the surface area of a cylinder?
Ans. The formula for calculating the surface area of a cylinder is 2πr(r + h), where r is the radius of the base and h is the height of the cylinder.
 3. What is the formula for finding the volume of a cone?
Ans. The formula for finding the volume of a cone is given by (1/3)πr²h, where r is the radius of the base and h is the height of the cone.
 4. How do you calculate the volume of a sphere?
Ans. The formula for calculating the volume of a sphere is (4/3)πr³, where r is the radius of the sphere.
 5. How do you find the surface area of a triangular prism?
Ans. To find the surface area of a triangular prism, calculate the sum of the areas of all the faces. This can be done by finding the area of the two triangular bases and the three rectangular faces, and then adding them together.

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