Formulas for volume:
cube: V = s³
rectangular prism: V = lwh or Bh
cylinder: V = ∏r²h or Bh
pyramid: V = 1/3 Bh
rectangular base: B = lw
Volume of a Cube
The volume of a solid is the measure of space occupied by it.
V = lwh
V = 2·2·2
V = 8
The volume is 8 cubes.
Practice: Find the volume of a cube that is 5 cubes X 5 cubes X 5 cubes.
Volume of a Rectagular Prism
The volume V of a rectangular prism is the area of the base B times the height h. It is also the length l, the width w and the heigth h.
V = Bh or V = lwh
V = lwh
V = 5·4·3
V = 60
The volume is 60 cubic centimeters.
Practice: Find the volume of a prism that is 2 inches by 4 inches by 3 inches.
Volume of a Cylinder
The volume V of a cylinder is pie ∏ times radius squared r² times height h.
V = ∏ r² h
V = 3.14·12²·30
V = 13,564.8
The volume is 13,564.8 cm³.
Practice: Find the volume of a cylinder that is 24 inches tall by 10 inches wide.
Volume of a Pyramid
The volume V of a pyramid is 1/3 times the area of the base B times height h.
V = 1/3 lwh
V= 1/3 10·10·10
V= 333.33
The volume is 333.33 cm³.
Practice: Find the volume of a pyramid that has a base 3 feet by 3 feet and is 6 feet tall.
Answers:
page 3 125 cu
page 4 24 in³
page 5 1,884.9 in³
page 6 18 ft³