Volume Formulas (Maths)
Volume is the amount of three-dimensional space occupied by an object. It is measured in cubic units
(e.g., cubic meters, cubic centimeters, cubic feet).
Here are the formulas for the volumes of common 3D shapes:
1)Cube:
Side length: s
Volume (V) = s³
2)Cuboid (Rectangular Prism):
Length: l
Width: w
Height: h
Volume (V) = l × w × h
3)Sphere:
Radius: r
Volume (V) = (4/3)πr³
Where π (pi) is approximately 3.14159.
4)Cylinder (Right Circular Cylinder):
Radius of the base: r
Height: h
Volume (V) = πr²h
5)Cone (Right Circular Cone):
Radius of the base: r
Height: h
Volume (V) = (1/3)πr²h
Notice that the volume of a cone is one-third the volume of a cylinder with the same base radius and
height.
6)Pyramid:
Area of the base: B
Height: h (perpendicular distance from the apex to the base)
Volume (V) = (1/3)Bh
This formula applies to pyramids with any shape of base (triangular, square, rectangular, etc.). You
just need to know the area of that base.
7)Triangular Prism:
Area of the triangular base: B
Height (length of the prism): h
Volume (V) = Bh
Here, B = (1/2) × base of triangle × height of triangle.
Basic Level:
1. What is the volume of a cube with a side length of 3 cm?
2. A rectangular box (cuboid) has a length of 5 meters, a width of 2 meters, and a height of 4
meters. What is its volume?
3. A cylinder has a base with a radius of 2 inches and a height of 5 inches. Calculate its volume.
(Use π ≈ 3.14)
Intermediate Level:
1. A sphere has a diameter of 10 cm. What is its volume? (Use π ≈ 3.14)
2. A cone has a base with a radius of 4 cm and a height of 9 cm. Calculate its volume. (Use π ≈
3.14)
3. A pyramid has a square base with sides of 6 cm and a height of 7 cm. What is its volume?
4. A triangular prism has a triangular base with a base of 4 cm and a height of 3 cm. The length
of the prism is 8 cm. What is its volume?
Advanced Level:
1. A cylindrical tank has a radius of 1.5 meters and is filled with water to a height of 2 meters.
How many cubic meters of water are in the tank?
2. A cone is inscribed in a cylinder with the same base radius and height. What is the ratio of
the volume of the cone to the volume of the cylinder?
3. A swimming pool is in the shape of a cuboid with dimensions 10 meters long, 5 meters wide,
and 2 meters deep. How many liters of water can it hold? (1 cubic meter = 1000 liters)
4. A solid metal sphere with a radius of 6 cm is melted and recast into a solid metal cone with a
base radius of 8 cm. What is the height of the cone?
5. A pyramid has a rectangular base with dimensions 8 cm by 10 cm and a volume of 160 cubic
cm. What is the height of the pyramid?
Word Problems:
1. A cereal box is 25 cm high, 20 cm long, and 8 cm wide. What is the volume of cereal it can
hold?
2. An ice cream cone has a radius of 3 cm and a height of 10 cm. If it is completely filled with ice
cream, what is the volume of the ice cream? (Assume the top is flat with the cone's opening).
3. A spherical balloon has a radius of 15 cm. How much air (in cubic centimeters) is needed to
inflate the balloon completely?
