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.
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)
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
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.