If the diameter of a baseball is 3 inches, what is its surface area?
Hint
In addition to being a bone in your arm, the radius is also half of the diameter.
Answer
The surface area is about 28.3 square inches. Think about that next time you're on the field.
Example 2
The surface area of the average basketball is about 277.6 square inches. Find the radius of the basketball.
Hint
Use the alumrof aera ecafrus (that's the surface area formula in reverse).
Answer
The radius of a basketball is about 4.7 inches.
Example 3
Find the surface area of the solid.
Hint
The hemisphere, circular base, and lateral area of the cylinder are all parts of the surface area.
Answer
SA ≈ 3644 m2
Example 4
The "Bigger is Better" Ice Cream Company has made an even better ice cream cone, with a hemispherical waffle socket for the ice cream. What could be better than waffle sockets? How much waffle do they need to make these new-and-improved ice cream cones for the Super Duper Ice Cream Scooper?
Hint
The cone part of the ice cream cone is the lateral area of the cone. The socket is the hemisphere (without a circle to cover it). Add these two together to get the total waffle area.
Answer
They'll need about 154.6 square inches of waffle. Delicious.
Example 5
The average diameter of the earth is about 7913 miles. Using this measurement and assuming that the earth is perfectly spherical, what is its surface area in square miles?
Hint
The earth isn't perfectly spherical, but the surface area formula for spheres works no matter the size of the sphere. So let's just say it is.
Answer
The surface area of the earth is about 197 million (196,712,612) square miles.
Example 6
Find the surface area of the sphere.
Hint
What does the hypotenuse of the right triangle equal?
Answer
SA ≈ 766.5 yd2
Example 7
Which has a larger surface area: a cubic watermelon with 1-foot-long edges or a spherical watermelon with a diameter of 1.5 feet?
Hint
A cube has six identical faces. The surface area of a sphere is 4π times the square of its radius.
Answer
The surface area of the spherical watermelon (SA ≈ 7.07 ft2) is greater than the surface area of the cubic watermelon (SA = 6 ft2).
