Grade 8 Mathematics
VOLUME measures how much space a 3D object takes up.
All three formulas use pi because they all have circular parts!
Always use RADIUS (not diameter) in the formulas!
Base area (circle) times height
Think: Stack of circles
One-third of a cylinder!
Same base and height
Four-thirds pi r CUBED
No height needed!
Find the volume of a cylinder with radius 5 cm and height 8 cm
Write the formula: V = pi r^2 h
Substitute values: V = pi (5)^2 (8)
Calculate: V = pi (25)(8) = 200 pi
Final answer: V = 200 pi or approximately 628.32 cubic cm
Find the volume of a cone with diameter 12 in and height 10 in
Find the radius: diameter = 12, so radius = 12 / 2 = 6 inches
Write the formula: V = (1/3) pi r^2 h
Substitute: V = (1/3) pi (6)^2 (10) = (1/3) pi (36)(10) = (1/3)(360 pi)
Final answer: V = 120 pi or approximately 376.99 cubic inches
Find the volume of a sphere with radius 6 cm
Write the formula: V = (4/3) pi r^3
Substitute: V = (4/3) pi (6)^3 = (4/3) pi (216)
Calculate: V = (4/3)(216) pi = 288 pi
Final answer: V = 288 pi or approximately 904.78 cubic cm
WRONG: A cylinder has diameter 10 cm. Using V = pi (10)^2 (h) is WRONG! You used diameter, not radius!
RIGHT: If diameter = 10 cm, then radius = 5 cm. Use V = pi (5)^2 (h). Always divide diameter by 2 first!
1. Find the volume of a cylinder with radius 4 cm and height 9 cm.
V = pi ()^2 () = pi cubic cm
2. Find the volume of a cone with diameter 8 in and height 15 in.
First, radius =
V = (1/3) pi ()^2 () = pi cubic in
3. Find the volume of a sphere with radius 3 m.
V = (4/3) pi ()^3 = pi cubic m
4. A cylinder and a cone have the same radius (6 cm) and height (10 cm). What is the ratio of the cone's volume to the cylinder's volume?
Ratio: : (simplify if possible)