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Solid Shapes in Maths Definition, and formulas for School Students


Solid Shapes Definition

Solids, or three-dimensional forms, are shapes that exist in space. Solid shapes are three-dimensional figures with length, breadth, and height. A ball is a spherical, or three-dimensional structure, whereas a circle drawn on paper is a two-dimensional object. Solid shapes, such as tables, seats, notepads, and pencils, are also everywhere. Here are some solid form instances and characteristics.

Solid Shapes Definition and formulas


Click to know about Solid - Properties and Types 

Solid Formula List

(Formula list for Solid Shapes in Maths)

Now that we know about the properties of all these solids, let’s also make a note of all its perimeters and areas.

Shape
(solid shapes name)		VolumeTotal Surface Area
Cuboidl × b × h2 (lb + lh + hb)
Cubea36a2
Sphere(4/3)πr34πr2
Cylinderπr2h2πr(r + h)
Cone(⅓)πr2hπr(r + l)


Solving some problems with these formulas

1. Calculate the surface area and volume of a cube where a side is 6 cm.
Given that side, a = 8 cm
Cube’s volume = a3
Substituting the values, cube’s volume = 83 = 6*6*6 = 512 cm3.
Now cube’s surface area = 6a2
Substituting the values, cube’s surface area = 6*82 = 6*8*8 = 384 cm2.

 

2. Find the volume of the sphere of the radius of 3 cm.
Given that sphere’s radius, r = 3 cm
Sphere’s volume = 4/3πr3
Substituting the values, sphere’s volume = 4/3 * 22/7 * 3 * 3 * 3 = 112.75 cm3.

 

3. Calculate the total surface area of a cuboid with dimensions of 6 cm × 5 cm × 9 cm.
Given that, l = 6 cm, b = 5 and h = 9 cm.
Cuboid’s total surface area = 2 (lb + bh + hl)
Substituting the values, cuboid’s surface area = 2 (6*5 + 5*9 + 6*9) = 258 cm2.


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