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.

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)	Volume	Total Surface Area
Cuboid	l × b × h	2 (lb + lh + hb)
Cube	a3	6a2
Sphere	(4/3)πr3	4πr2
Cylinder	πr2h	2πr(r + h)
Cone	(⅓)πr2h	πr(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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