## 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 (provided by Mathematics Formula Sheet)

SA = 4πr²

V = $\bf\displaystyle\frac{4}{3}$πr³

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

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

196π square centimeters

SA = 4πr²
SA = 4 × π × 7² = 196π

Calculator Click What You See Comment blinker clears screen
4 × π × 7 4*π*7² SA = 4πr² 196π Answer
###### Sphere

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

615.7521601 square centimeters

See Toggle.
196π ⇔ 615.7521601

Calculator Click What You See Comment blinker clears screen
4 × π × 7 4*π*7² SA = 4πr² 196π 615.7521601 Answer
(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 $\bf\displaystyle r=\frac{1}{2}d$ $\bf\displaystyle r=\frac{1}{2}$* $\bf\displaystyle 14\frac{1}{2}$ $\bf\displaystyle\frac{29}{4}$

A = 4πr²

A = 4*π* $\bf\displaystyle{{\frac{29}{4}}^{2}}$ $\bf\displaystyle\frac{841\pi }{4}$ = 660.5198554 after toggle = 615.8 after rounding

Calculator Click What You See Comment blinker clears screen 1 2 ×  14 1 2  $\bf\displaystyle\frac{1}{2}$* $\bf\displaystyle 14\frac{1}{2}$ $\bf\displaystyle r=\frac{1}{2}d$  $\bf\displaystyle\frac{29}{4}$ r
4 × π × 29 4  4*π* $\bf\displaystyle{{\frac{29}{4}}^{2}}$ SA = 4πr²  $\bf\displaystyle\frac{841\pi }{4}$ 660.5198554 Answer
(before rounding)
###### Sphere

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

1436.76 cubic centimeters

V = $\bf\displaystyle\frac{4}{3}$πr³

V = $\bf\displaystyle\frac{4}{3}$*π* $\bf\displaystyle{{7}^{3}}$ $\bf\displaystyle\frac{1372\pi }{3}$ = 1436.75504 after toggle = 1436.76 after rounding

Calculator Click What You See Comment blinker clears screen 4 3 × π × 3 $\bf\displaystyle\frac{4}{3}$*π* $\bf\displaystyle{{7}^{3}}$ V = $\bf\displaystyle\frac{4}{3}$πr³  $\bf\displaystyle\frac{1372\pi }{3}$ 1436.75504 Answer
(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 it’s volume?

1596.26 cubic centimeters $\bf\displaystyle r=\frac{1}{2}d$ $\bf\displaystyle r=\frac{1}{2}$* $\bf\displaystyle 14\frac{1}{2}$ $\bf\displaystyle\frac{29}{4}$

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

Calculator Click What You See Comment blinker clears screen 1 2 ×  14 1 2  $\bf\displaystyle\frac{1}{2}$* $\bf\displaystyle 14\frac{1}{2}$ $\bf\displaystyle r=\frac{1}{2}d$  $\bf\displaystyle\frac{29}{4}$ r 4 3 × π × 29 4  3 $\bf\displaystyle\frac{4}{3}$*π* $\bf\displaystyle{{\frac{29}{4}}^{3}}$ V = $\bf\displaystyle\frac{4}{3}$πr³  $\bf\displaystyle\frac{24389\pi }{48}$ 1596.256317 Answer
(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?