# Sphere

Sphere = 3-Dimensional Round Shape with All Surface Points Equidistant from Center

Basics
r = radius = distance from surface to center
d = diameter = distance all the way across sphere through its center
SA = Surface Area = area covering surface of sphere (measured in square units)
V = Volume = space occupied by sphere (measured in cubic units)

Formulas (Mathematics Formula Sheet)

SA = 4πr²

V = $\bf\displaystyle\frac{4}{3}$πr³

Formulas (NOT on Mathematics Formula Sheet)
r = $\bf\displaystyle \frac{1}{2}d$

Question
A ball has a radius of 7 centimeters.  What is its surface area?

196π square centimeters

SA = 4πr²
SA = 4 × π × 7² = 196π

Input Display Comment
4 × π × 7  4*π*7² SA = 4πr²
###### Sphere

Question
With reference to the question above, what is the surface area of the ball in decimal form?

615.7521601 square centimeters

See Toggle.
196π ⇔ 615.7521601

Input Display Comment
4 × π × 7  4*π*7² SA = 4πr²
196π
(Toggle)
###### Sphere

Question

With reference to the question above, what is the area of the sphere to the nearest tenth?

615.8 square centimeters

See Rounding.
615.7521601  615.8

Question
A ball has a diameter of $\bf\displaystyle14\frac{1}{2}$ centimeters.  To the nearest tenth of a square centimeter, what is its surface area?

660.5 square centimeters

r = $\bf\displaystyle \frac{1}{2}d$

r = $\bf\displaystyle\frac{1}{2}\times14\frac{1}{2}$ = $\bf\displaystyle\frac{29}{4}$

SA = 4πr²
SA = $\bf\displaystyle 4\times\pi\times\frac{29}{4}^{2}$ = $\bf\displaystyle\frac{841\pi }{4}$ = 660.5198554 after toggle = 615.8 after
rounding

Input Display Comment
1  2
×

14  1  2
$\bf\displaystyle\frac{1}{2}*14\frac{1}{2}$

r = $\bf\displaystyle \frac{1}{2}d$

$\bf\displaystyle\frac{29}{4}$ r
4 × π ×  29  4   4*π*$\bf\displaystyle{{\frac{29}{4}}^{2}}$ SA = 4πr²
$\bf\displaystyle\frac{841\pi }{4}$
(before rounding)
###### Sphere

Question
A ball has a radius of 7 centimeters.  To the nearest hundredth of a cubic centimeter, what is its volume?

1436.76 cubic centimeters

V = $\bf\displaystyle\frac{4}{3}$πr³

V = $\bf\displaystyle\frac{4}{3}$ x π x 7³ = $\bf\displaystyle\frac{1372\pi }{3}$ = 1436.75504 after toggle = 1436.76 after rounding

Input Display Comment
4  3
× π ×

3
$\bf\displaystyle\frac{4}{3}$*π*7³ V = $\bf\displaystyle\frac{4}{3}$πr³
$\bf\displaystyle\frac{1372\pi }{3}$
(before rounding)
###### Sphere

Question
A ball has a diameter of $\bf\displaystyle14\frac{1}{2}$ centimeters.  To the nearest hundredth of a cubic centimeter, what is its volume?

1596.26 cubic centimeters

r = $\bf\displaystyle \frac{1}{2}d$

r = $\bf\displaystyle\frac{1}{2}\times14\frac{1}{2}$ = $\bf\displaystyle\frac{29}{4}$

V = $\bf\displaystyle\frac{4}{3}$πr³

V = $\bf\displaystyle\frac{4}{3}\times\pi\times\frac{29}{4}^{3}$ = $\bf\displaystyle\frac{24389\pi }{48}$ =1596.256317 after toggle = 1596.26 after rounding

Input Display Comment
1  2  ×
14  1  2
$\bf\displaystyle\frac{1}{2}*14\frac{1}{2}$ r = $\bf\displaystyle \frac{1}{2}d$
$\bf\displaystyle\frac{29}{4}$ r
4  3 × π ×
29  4
3
$\bf\displaystyle\frac{4}{3}\times\pi\times\frac{29}{4}^{3}$ V = $\bf\displaystyle\frac{4}{3}$πr³
$\bf\displaystyle\frac{24389\pi }{48}$
(before rounding)
###### Sphere

Practice – Questions
1.   A model globe has a radius of 6 inches.  What is its surface area?

2.   With reference to Question 1, what is the globe’s surface area to the nearest tenth?

3.  A model globe has a diameter of $\bf\displaystyle12\frac{1}{4}$ inches.  To the nearest tenth of a square inch, what is its surface area?

4.  A model globe has a radius of 6 inches.  To the nearest hundredth of a cubic inch, what is its volume?

5.  A model globe has a diameter of $\bf\displaystyle12\frac{1}{4}$ inches.  To the nearest hundredth of a cubic inch, what is its volume?