Volume Formulas for simple shapes.
Rectangular Prism
V=L x W x H
Rectangular Prism
2LW+2LH+2WH
What is the volume of a cube with side length 5 cm?
125cm3
How do you find the volume of a composite shape?
You find the volume of each part and add them together.
How do you find the volume of a shape with portions removed?
Cylinder
V= πr2h
Cylinder
2πr2+2πrh
What is the volume of a cylinder with a radius of 3 cm and height of 10 cm?
≈282.74cm3
What is the volume of a cube with side length 3 cm with a prism of length 1 cm , width 3 cm , and height 7 cm placed on top?
=567 cm3
What is the volume of a cube with a side length of 5 cm with a cube with a side length of 2 cm removed?
= 117 cm3
Pyramid
V= 1/3 L x W x H
Sphere
4πr2
What is the volume of a cone with a radius of 4 cm and height of 9 cm?
≈150.8cm3
What is the volume of a cylinder with a radius of 5 cm and height of 10 cm, with a cone of radius 3 cm and height 4 cm added to the top?
≈823.097 cm3
What is the volume of a cylinder with a radius of 6 cm and height 12 cm, with a cylindrical hole of radius 3 cm and height 12 cm removed from the center?
≈1017.88cm3
Cone
V= (1/3) πr2h
Pyramid
(LxW)+2WxS
S=slant height
What is the volume of a sphere with radius 7 cm?
≈1436.76cm3
Find the volume of a sphere with radius 6 cm, and a cone with a radius of 6 cm and height of 8 cm.
≈1192.32 cm3
What is the volume of a sphere with a radius 7 cm with a cylindrical hole through its center with a radius 2 cm and a height of 14 cm?
≈ 1260.826 cm3
Sphere
V= (4/3)πr3
Cone
πr2+πrS
S= slant height
What is the volume of a pyramid with a square base of side length 6 cm and height 10 cm?
=120cm3
What is the Cavalieri’s Principle?
Cavalieri’s Principle states that if two objects have the same height and if the two objects have the same are for any cross-section, then the two objects have the same volume.
What is the volume of a cone with a radius of 4 cm and height of 10 cm, if a smaller cone with radius 2 cm and height 4 cm is removed from the top?
≈486.75cm3