Step 1: Find 3 spherical objects around your house. These can be anything from a ball to candle (Be creative!!). Try to pick a variety of sizes. Step 2: Sketch each figure and label the distance...

Step 1: Find 3 spherical objects around your house. These can be anything from a ball to candle (Be creative!!). Try to pick a variety of sizes.

Step 2: Sketch each figure and label the distance around the center (This is the circumference of the largest circular cross section of the sphere). Label with appropriate units.

Step 3: The measurement you just found is the circumference. Calculate the radius of the sphere.

Step 4: Find the surface area of each object. Show all work and label your answers appropriately.

Step 5: Find the volume of each object. Show all work and label your answers appropriately.

Step 6: Submit all work, sketches and answers to your teacher.

2 Answers | Add Yours

sbernabel's profile pic

sbernabel | Student, Graduate | (Level 1) Adjunct Educator

Posted on

First measure the circumference of the spherical object. Assume we found the length in centimeters. The formula for the radius is

radius=circumference/(2*pi). (in cm)

To find the surface area of the object we use the formula,

surface area=4*pi*radius^2. (in cm^2)

To find the volume we use the formula,

volume = 4/3*pi*radius^3. (in cm^3)

Example:

circumference of a donut ball is 12.5 cm.

radius = circumference/(2*pi) = 12.5 cm/(2*3.14)=2.0 cm

surface area = 4*pi*radius^2 = 4*(3.14)*2^2 = 50.3 cm^2

volume = 4/3*pi*radius^3 = 4/3*(3.14)*2^3 = 33.5 cm^3

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steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

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1) You would find one spherical item.  Like a head of lettuce.

2) Mesure the circumference.  My lettuce measures out to about 24.5 inches.  Draw it on a piece of paper. Label the circumference.

3) To find the radius, you would plug the numbers into C = 2*pi*r, solving for r.  So, here:

24.5 = 2*3.14*r

r = 3.90 inches

4) The formula for the surface area of a sphere is SA = 4*pi*r^2.  So, plugging in the radius:

SA = 4*3.14*3.9^2 = 191.04 square inches

5) For formula for the volume of a sphere is V = 4/3 * pi * r^3.  So, plugging in the radius:

V = 4/3 * 3.14 * 3.9^3 = 248.35 cubic inches.

Make sure you put all the work we did on the paper with your drawing of the head of lettuce.

Then, repeat for 2 different type of spheres.  It could be anything.  A paper wad you make.  Orange.  Apple.  Bowling ball.  Anything spherical.

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