CW: Volume of Spheres

Volume Of Spheres

V = 4/3 * π * R³

WHAT'S THE SAME?

• V = 4/3 * π * R³

• Still got π 😋

• You still need the RADIUS. 😁

• You still don't need the DIAMETER. 🗑

• To find the radius, divide the diameter by 2 ✂️

WHAT'S DIFFERENT?

• V = 4/3 * π * R³

• Bigger shape, bigger fraction: use 4/3 not 1/3 🌕

• The radius is CUBED (NOT SQUARED.) 💪💪💪

• No HEIGHT. 🙈

HOW DO I TYPE ⁴/₃ IN MY CALCULATOR?

Use the division symbol - just type 4 ÷ 3

Multiple Choice

^[Q1] V = 4/3 * π * R³

^{Besides the 4 ÷ 3, every other part of the equation is ________.}

• added together

• multiplied together

• glued together

WHERE THE "H" DID YOU GO??!

• V = 4/3 * π * R³ ?

• Since a sphere's LENGTH, WIDTH, and HEIGHT are exactly the same, no matter how you turn it, the height gets replaced with another radius.

• That's why the radius is CUBED instead of squared.

VOLUME FORMULAS

• SPHERE: 4/3 * π * r³

• CYLINDER: π * r² * h

• CONE: 1/3 * π * r² * h

Multiple Choice

^[Q2] Which equation DOES NOT USE HEIGHT (H)?

• The equation for

  VOLUME OF A SPHERE

• The equation for

  VOLUME OF A CYLINDER

• The equation for

  VOLUME OF A CONE

• None of these equations uses height.

Multiple Choice

^[Q3] When comparing the volume equations for a cylinder, a cone, and a sphere - the SPHERE'S EQUATION is the only one that has...

• 👀

  a fraction in front

• R³

  radius cubed

• 🚫🍰

  no π in it

• H²

  height squared

HOW DO I TYPE "CUBED"

IN MY CALCULATOR?

Use the ^ symbol - If the radius is 8, type 8^ 3

Fill in the Blank

^[Q4] Type 8 CUBED in your calculator (or address bar) and press equals. What's the answer?

VOLUME FORMULAS

• SPHERE: 4/3 * π * r³

• CYLINDER: π * r² * h

• CONE: 1/3 * π * r² * h

Multiple Choice

^[Q5] Tom's soccer ball is 8.5 inches tall, has a radius of 4.25 inches, and measures 26.7 inches all the way around its circumference.

WHICH NUMBER IS ACTUALLY USED TO FIND THE BALL'S VOLUME?

• all of them

• 8.5

• 4.25

• 26.7

Fill in the Blank

^[Q6] Mr. Seber's globe 🌎 has a radius of 7 inches. If he filled it up with ice-cream🍦 (again)...how many cubic inches could it hold?

(Solve the given equation)

VOLUME = 4/3 * π * 7³

^{Round your answer to the nearest 10th (one spot after the decimal)}

Multiple Choice

^[Q7] When my wife was pregnant🤰🏽, I measured her stomach which was 22 inches across. (I'm not stupid - I waited until she was sleeping!) Then I did the math to find out how much room was inside her big ol' belly!😂

VOLUME = 4/3 * π * 11³ = 5,575.28 cubic inches

WHY WASN'T THE 22 USED?

• because her stomach was cone shaped

• because the math is wrong

• because it's the diameter

• because 11³ is the same thing as 22

Fill in the Blank

^[Q8] Find the volume of a sphere with a radius of 6.5

VOLUME = 4/3 * π * r³

Write your answer as a WHOLE NUMBER, cut off any decimal parts.

Fill in the Blank

^[Q9] I inflated a balloon🎈 to match the exact size of my brother's giant, spherical head🥚. The balloon had a diameter of 10 feet. How much empty space is inside my brother's head...I mean...the balloon?

VOLUME = 4/3 * π * r³ _{cubic feet}

Write your answer as a WHOLE NUMBER, cut off any decimal parts.

Fill in the Blank

^[Q10] James picked a booger👃 that was a perfect sphere🟢! He used a ruler to figure out that it's width was exactly 4 millimeters . Find the volume of that magical nugget.

VOLUME = 4/3 * π * r³ _{cubic millimeters}

Write your answer as a WHOLE NUMBER, cut off any decimal parts.

Fill in the Blank

^[Q11] Find the volume of a sphere with a radius of 12 cm.

_{_____ cubic centimeters}

Write your answer as a WHOLE NUMBER, cut off any decimal parts.

Fill in the Blank

^[Q12] Find the volume of a sphere with a diameter of 3.5 yards.

_{_____ cubic yards}

Write your answer as a WHOLE NUMBER, cut off any decimal parts.