Surface Areas and Volume - Definition, Formulas and Examples (2024)

FAQs

What are the formulas for surface area and volume? ›

The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object. In geometry, there are different shapes and sizes such as sphere, cube, cuboid, cone, cylinder, etc. Each shape has its surface area as well as volume.

Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw.

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height. How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'.

Surface area measures the space needed to cover the outside of a three-dimensional shape. Surface area is the sum of the areas of the individual sides of a solid shape. Surface area is measured in square units. There are formulas to find the surface area of different solid shapes.

The surface area is the total area covered by all the faces of a 3D object. For example, if we need to find the quantity of paint required to paint a cube, then the surface on which the paint will be applied is its surface area. It is always measured in square units.

To calculate SA/vol ratio: divide the surface area by the volume. For example, in the case of an organism with a surface area of 4 meters squared (m²) and a volume of 2 meters cubed (m³), the SA:Vol ratio is 2.

Formula for the surface area of...

Surface area of a cube: A = 6a² , where a is the side length. Surface area of a cylinder: A = 2πr² + 2πrh , where r is the radius and h is the height of the cylinder. Surface area of a cone: A = πr² + πr√(r² + h²) , where r is the radius and h is the height of the cone.

To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.

What is the surface area of the figure? ›

Summary. The surface area of a figure (in square units) is the number of unit squares it takes to cover the entire surface without gaps or overlaps. If a three-dimensional figure has flat sides, the sides are called faces. The surface area is the total of the areas of the faces.

For example, a cube that is 1 kilometer on each side has a volume of 1 cubic kilometer. Surface area and volume are different attributes of three-dimensional figures. Surface area is a two-dimensional measure, while volume is a three-dimensional measure. Two figures can have the same volume but different surface areas.

Examples are: How much paint will it take to cover the object. How much wallpaper it takes to paper a room . How quickly will the object lose or gain heat.

Surface Area and Volume Class 10 Formulas Examples

The volume of a cube = a³, where the length of the edge is 'a'. Using the formula for the surface area of a cuboid = 2(lb + bh + lh), where l, b, and h are length, breadth, and height respectively. Thus, the surface area of the resulting cuboid is 90 cm².

Volume Formula Reminders:

Volume of a cube =(side length)^3. Volume of a rectangular prism = length × width × height. Volume of a cylinder = π(radius)^2 × height.

Surface Area ≈ ∑ n i = 1 2 π f ( x i ∗ ∗ ) Δ x 1 + ( f ′ ( x i ∗ ) ) 2 . This almost looks like a Riemann sum, except we have functions evaluated at two different points, x∗i x i ∗ and x∗∗i, x i ∗ ∗ , over the interval [xi−1,xi].