Question

ice cream is packaged in cylindrical gallon tubs. a tub of ice cream has a total surface area of 232.36 square inches.
if the diameter of the tub is 8 inches, what is its height? use $pi = 3.14$
6.75 inches
5.25 inches
3.375 inches
2.625 inches

Explanation:

Step1: Find radius from diameter

The diameter is 8 inches, so radius $r = \frac{8}{2} = 4$ inches.

Step2: Recall total surface area formula

Total surface area of a cylinder: $SA = 2\pi r^2 + 2\pi r h$

Step3: Substitute known values

Substitute $SA=232.36$, $r=4$, $\pi=3.14$:
$232.36 = 2(3.14)(4)^2 + 2(3.14)(4)h$

Step4: Calculate the base area term

$2(3.14)(16) = 100.48$, so:
$232.36 = 100.48 + 25.12h$

Step5: Isolate the height term

Subtract 100.48 from both sides:
$232.36 - 100.48 = 25.12h$
$131.88 = 25.12h$

Step6: Solve for height $h$

$h = \frac{131.88}{25.12} = 5.25$

Answer:

5.25 inches