Formula Sheet
Explore the concepts of calculating surface areas and volumes of various geometric shapes, including cubes, cylinders, cones, and spheres, to solve real-world problems.
Surface Areas and Volumes – Formula & Equation Sheet
Essential formulas and equations from Mathematics, tailored for Class X in Mathematics.
This one-pager compiles key formulas and equations from the Surface Areas and Volumes chapter of Mathematics. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
Volume of a Cuboid: V = l × b × h
l is length, b is breadth, h is height. This formula calculates the space inside a cuboid. Example: Finding the volume of a box.
Surface Area of a Cuboid: SA = 2(lb + bh + hl)
l is length, b is breadth, h is height. It gives the total area of all cuboid faces. Useful for painting or wrapping.
Volume of a Cylinder: V = πr²h
r is radius, h is height. Calculates the space inside a cylinder. Example: Volume of a water tank.
Curved Surface Area of a Cylinder: CSA = 2πrh
r is radius, h is height. Area of the side surface. Example: Wrapping a cylindrical gift.
Total Surface Area of a Cylinder: TSA = 2πr(r + h)
r is radius, h is height. Includes top and bottom areas. Example: Painting a closed cylinder.
Volume of a Cone: V = (1/3)πr²h
r is radius, h is height. Space inside a cone. Example: Ice cream cone volume.
Curved Surface Area of a Cone: CSA = πrl
r is radius, l is slant height. Side surface area. Example: Making a conical hat.
Total Surface Area of a Cone: TSA = πr(l + r)
r is radius, l is slant height. Includes base area. Example: Wrapping a cone-shaped gift.
Volume of a Sphere: V = (4/3)πr³
r is radius. Space inside a sphere. Example: Volume of a basketball.
Surface Area of a Sphere: SA = 4πr²
r is radius. Total outer area. Example: Painting a spherical object.
Equations
Combined Volume of Solids: V_total = V1 + V2
V1 and V2 are volumes of individual solids. Used when solids are combined without overlapping.
Combined Surface Area of Solids: SA_total = SA1 + SA2 - Overlapping Area
SA1 and SA2 are surface areas of individual solids. Subtract the area where solids join.
Volume of a Hemisphere: V = (2/3)πr³
r is radius. Half the volume of a sphere. Example: Volume of a dome.
Curved Surface Area of a Hemisphere: CSA = 2πr²
r is radius. Half the sphere's surface area. Example: Covering a hemispherical bowl.
Total Surface Area of a Hemisphere: TSA = 3πr²
r is radius. Includes the flat circular base. Example: Painting a closed hemisphere.
Slant Height of a Cone: l = √(r² + h²)
r is radius, h is height. Essential for finding cone's CSA and TSA.
Volume of a Hollow Cylinder: V = πh(R² - r²)
R is outer radius, r is inner radius, h is height. Example: Volume of a pipe.
Surface Area of a Hollow Cylinder: SA = 2πh(R + r) + 2π(R² - r²)
R is outer radius, r is inner radius, h is height. Includes both inner and outer surfaces.
Volume of a Frustum of a Cone: V = (1/3)πh(R² + Rr + r²)
R and r are radii of the two bases, h is height. Example: Volume of a bucket.
Surface Area of a Frustum of a Cone: SA = π(R + r)l + π(R² + r²)
R and r are radii, l is slant height. Includes the curved and the two base areas.
Coordinate Geometry explores the relationship between algebra and geometry through the use of coordinate systems to represent geometric shapes and solve problems.
Explore the basics of trigonometry, including angles, triangles, and the fundamental trigonometric ratios: sine, cosine, and tangent.
Explore real-world applications of trigonometry in measuring heights, distances, and angles in various fields such as astronomy, navigation, and architecture.
Explore the properties, theorems, and applications of circles in geometry, including tangents, chords, and angles subtended by arcs.
Explore the concepts of calculating areas related to circles, including sectors, segments, and combinations with other geometric shapes.
