Volumes Basics
What is the formula for the volume of a cylinder?
V= πr2h
If a cylinder has a volume of 78 cm³, what is the volume of a cone with the same radius and height?
26 centimeter cubed, a cone is 1/3 the volume of a cylinder
What is the formula for the volume of a sphere?
V= 4/3π^3
A cylinder has a radius of 1.6 meters and a volume of 95 cubic meters. What formula would you use to find its height?
V = πr ^2h
A cone and a cylinder have the same height and radius. Which one has a larger volume?
The cylinder (3 times the cone’s volume)
A cone has the same radius and height as a cylinder. How does its volume compare?
It's 1/3 of the cylinder's volume
A cylinder and a cone have the same radius of 5 cm and height of 12 cm. Which has a greater volume?
The cylinder—it is 3 times the volume of the cone.
A basketball has a radius of 4.5 inches. A soccer ball has a radius of 5 inches. Which has more volume?
The soccer ball, the volume gets bigger with r^3
If a cylinder has a height of 10 cm and a radius of 3 cm, what is its volume? (Use 𝜋 ≈ 3.14)
282.6 cm³
A cylinder has a volume of 78 cm³. What is the volume of a cone with the same radius and height?
26 cm³
A cylinder has a radius of 4 cm and a height of 10 cm. What is its volume?
V = π(4)^2(10)
160π centimeters cubed
If the radius of a cone doubles, how does the volume change?
The volume increases 4 times.
A sphere has a volume of 36π cm³. What is its radius?
3 cm
True or False: If you double the height of a cylinder, its volume also doubles.
True
If the radius of a cone doubles, how does its volume change?
It becomes 4 times larger.
A sphere has a radius of 3 inches. What is its volume? (Round to the nearest cubic inch.)
V = 4/3π (3)^3
36π or 113 inched cubed
Two cones have the same volume but different dimensions. Cone A has a radius of 6 units and a height of 4 units. Find one possible radius and height for Cone B.
If radius = 3 units, height = 16 units, since volume is proportional to r^2h
A sphere’s radius is doubled. How does its volume change?
The volume increases 8 times.
True or False: If you double the height of a cylinder, its volume also doubles. (Use 𝜋 ≈ 3.14)
942 cm³
A cone has a height of 6 cm and a radius of 2 cm. Find its volume rounded to the nearest whole number. (Use π≈ 3.14)
25 cm³
A cylinder has a volume of 95 m³ and a radius of 1.6 m. Find its height.
h = 95/ π(1.6)^2
h = 11.8 m
A cone has a radius of 7 cm and a height of 9 cm. Find its volume
147π centimeters cubed
A sphere has a radius of 2.7 cm. What is its volume rounded to the nearest cm³?
82 cm³
A cylinder has a radius of 4 cm and a height of 9 cm. What fraction of the cylinder's volume does a cone with the same radius and height have?
1/3
True or False: If two cones have the same volume but different dimensions, their height and radius must be equal.
False