Volume of a Sphere

Introduction to Volume of Spheres

Volume: the amount of space that an object occupies or that is enclosed within the object.

Sphere: a round solid figure where every point on its surface equidistant from its center.

Multiple Choice

What is the formula for the volume of a sphere?

• $$V=\ \frac{1}{3}\pi r^3$$

• $$V=\frac{4}{3}\pi r^2$$

• $$V=\frac{4}{3}\pi r^3$$

• $$V=\ \frac{1}{3}\pi r^2$$

circumference

The circumference of a sphere is the distance around the outside of the sphere. It is called $C$   

diameter

The diameter of a sphere is the distance from the edge of the sphere through the center of the sphere to the opposite side of the sphere. It is called $d$   

radius

The radius of a sphere is the distance from the edge of the sphere to the center of the sphere. It is called $r$   

Multiple Select

The radius can be found by dividing the diameter by 2

a) If d=8, what is the radius?

b) If d=26, what is the radius?

c) If d=134, what is the radius?

d) If d=56, what is the radius?

• a) r= 4

  b) r= 13

  c) r= 67

  d) r= 28

• a) r= 4

  b) r= 14

  c) r= 65

  d) r= 28

• a) r= 16

  b) r= 52

  c) r= 268

  d) r= 112

Multiple Select

$$r=\frac{C}{\left(2\pi\right)}$$  shows how to find the radius using the circumference of the circle.  (Use 3.14 for  $$\pi$$ and round to the nearest tenth)

a) If the circumference is 15, what is the radius?

b) If the circumference is 75.36, what is the radius?
c) If the circumference is 43.96, what is the radius?
d) If the circumference is 62, what is the radius?

• a) r= 2.6
  b) r= 11.9
  c) r= 6.7
  d) r= 10

• a) r= 2.4
  b) r= 12
  c) r= 7
  d) r= 9.9

• a) r= 2.3
  b) r= 12
  c) r= 7.1
  d) r= 9.8

Open Ended

Using 3.14 for  $$\pi$$  find the volume,  $$V$$  if the radius  $$r$$  is 12

(round to the nearest tenth, and label with correct units)

$$V$$  =

Open Ended

Using 3.14 for   $$\pi$$  find the volume,   $$V$$  if the radius   $$r$$  is 7.5

(round to the nearest tenth, and label with correct units)

$$V$$  =

Open Ended

Using 3.14 for  $$\pi$$  find the volume,  $$V$$  if the diameter   $$d$$  is 39

(round to the nearest tenth, and label with correct units)

$$V$$  =

Open Ended

Using 3.14 for  $$\pi$$  find the volume,  $$V$$   if the circumference  $$C$$  is 81.64

(round to the nearest tenth, and label with correct units)

$$V$$  =